Hello!

I've been learning to play the piano since two months now.
Whenever I try to play any moderate song, this is what happens:
When I play only treble: Perfect
When I play only base: Perfect
When I play both simultaneously: Disaster

How do I improve the co-ordination between left hand and right hand?
Even when base and treble are going at different pace I have this tendency to mingle up the two. My left hand actually tends to imitate the finger movements of my right hand.
Is it just me or you've also experienced this? How did you cope up?

Go as slow as necessary to be able to do it.

For example, slow as in one beat every 10 seconds.

Also, ask your teacher for help with this. Hands Together is a common piano playing obstacle, and most teachers are skilled in helping people with this.

Also you could try focusing on when the hands play alone and when they are together, instead of counting. This is sort of a "follow the bouncing ball" concept. So for a simple example, a song could go. Together, Right, Together, Left, Right, Together, Rest, Together... etc

Don't worry too much about the rhythm to start, you've already done that with hands separate. It's more about the coordination at first.

Believe it or not, there are actually different kinds of "disaster". Knowing which one can go a long way towards solving your specific issues. Since you're a beginner-beginner, meaning very fresh to the piano (under six months), I would infer it is one of a few basic things that should work themselves out as you become more familiar with the way the hands move, the position of the keys, etc. Some may not, but that is a separate issue. (I am avoiding naming anything, because it probably won't help and may hurt more than help, but I will name one idea.)

Typically, the coordination issue happens because there are left/right movements, in/out movements, and up/down movements. Sometimes the hands move in parallel, and sometimes they move opposite each other. When they're moving together or when they're moving opposite, it's much easier to coordinate. But when they are constantly flip-flopping, this is when problems occur. (And the hands flip-flop more than they align.) There are specific techniques that help you to understand these movements better, but I am afraid I would confuse the heck out of you if I just started rattling things off with only 2 months under your belt. For now, I will say this:

rocket's advice is very good. If you can post up some videos, we may be able to get more specific. Otherwise, about the best thing we can offer is to say, "Go slower."

What I do is:
-Work on each measure at first, and then go for the whole phrase. If you are working on binary rithms this is very easy to do (though first weeks are a nightmare, you'll do it well soon!). Besides, beginner's sheets usually are oriented to learn movement patterns, which are simple and logical.
Try to find the logic in it, try to get relaxed, trust your brain.
-One thing that helps me a lot is to close my eyes and point my attention towards an imaginary target right in front of me (I should look at the sheet, but pieces are so simple now), I mean not paying attention to any of both hands, but to the work they do together.
So, work slower; work on one single measure/pattern until you get it; aim to the center;try to flow.(and then pray if you are the kind, or just go to sleep, your brain will do the rest).
As many others have already said, practice time is when we send data to our brains, so we'd better sending them well.

Sounds like you need to break your music down into smaller sections. So maybe work on bar to bar or do in sections of 4 bars. If the Bass section has quite a bit going on at the same time as the treble then I'd suggest taking the first note in the bass or the note that sounds like it fits best and playing that at the start of the abr and holding down for the length of the bar i.e. if in 4/4 then hold for 4. Once it changes up in the bass then change up but as a single note held out throughout the bar.

Once we have developed the co-ordination like this as a simple arrangement and are confident of this you can then start adding in more parts.

Hope this helps!

I found one thing that really helped get me to deal with The Great Hands Together Problem (after 30+ years away from a keyboard) was doing some pieces where the hands share the load. In other words, where the LH always alternates notes with the RH (they never play at the same time), to create a single melody. There are probably pieces you can find at different levels that do this. [I used Bach's Preludes 846 and 999, played quite slowly, but there will be other simpler pieces that do much the same.]

I found this was a really good stepping stone, that (after learning a couple of such pieces) allowed me to then read and play both hands simultaneously.

I think part of the issue here is that you are not only having to play two hands at once, but also you are having to read two lines of music at once. Lots of stuff happening at the same time.

So, this stepping stone reduces slightly the cognitive load, as the notes are always consecutive on the page, and struck consecutively rather than simultaneously (until the final chord). And then a speeded-up consecutive approaches simultaneous.

I know it is frustrating but it will get better. As others have said, go slow. After 5 years of learning, even I have to work on seperate hands first especially on unfamiliar pieces.

You wait until you have to do scales with both hands together. Practice makes perfect.

And your HT disaster is probably quite different that when you can't play HS!