The question is in the title. I play as zerg most of the time and I have almost no idea what to do against the terran marine-marauder-medic combo in 2v2. The normal 1v1 strategy (banelings, basically) doesn't seem to work against these masses.
What you can do is get Infestors. Several of them would be ideal. When the MMM mass bunch up, drop fungal growth on them. Then burrow your infestors so they don't take damage and spam infested marines as quickly as possible (they're cheap energy so several infestors can create a mass of them quickly). Also, burrowed infestors can still spawn Infested Terrans. This is also assuming you have other units with your infestors. Roaches get kited pretty easily with Mauraders but if you use fungal growth that won't happen.
If they're a heavier Maruader build with few marines then Mutalisks will be the best counter. But don't relay heavily on them after you take out the first wave of Marauders because a smart opponent will switch to heavy marines and vikings if he sees you've gone mutas.
Marines in SC2 seem to be almost impossible to beat when there are enough of them, especially with marauder support, so your best chance is to destroy his supply and his reinforcements with drops, mutalisks or nydus worms while slowly killing his troops with suprise banelings (don't forget they can burrow, quite deadly if they jump out in the middle of a ball of marines) and hit-and-run tactics. Infestors work quite well, too, but if he has enough medics it will just slow him.
An MMM Ball moves relatively slowly so harassing his workers with some mutas and killing the marines that move from his base to his main unit ball should work quite well to prevent him to get enough reinforcements to fill his losses. In the worst case he has to keep half his army in his base to prevent your harass, which gives you an significant advantage at the front.
I do not recommend a frontal assault, even if you have a big ball of units yourself. It will cost a lot and then all of you just have to fill your losses and repeat from step 1. It's cheaper to hit-and-run, even if you have to sacrifice an expansion, just make sure you always have more expansions than your enemy.
Obviously this depends on what your team mate is doing, you guys should be working together with scouting and communicating what the enemy is sending at you. If it's marine/marauder banelings and speedlings should definitely work if executed properly. Also infestors can turn the tide of a battle quickly. Beyond that, try to directly target the medivacs with some anti-air so that the healing support can be eliminated.
Usually the scouting in 2s is so bad you can get away with a baneling bust. If they have a solid wall (no reactors, techlabs or supply depots as vital parts of the wall) you will have to resort to hydras. The MMM ball is a whole lot more effective than your hydras but you have the macro advantage. Make sure you have one more exp than the terrans and that you spread creep everywhere. You will need that creep as the terran ball will move faster than your hydras off creep. If your macro is any good you should have a higher food count than the terran. Also mix in some infestors and fungal growth as many marines as possible.
You can't assault a tank position with hydras though. So if there are tanks you will have to resort to doom dropping to destroy their production.
It's not going to be easy, and it will feel like the terran army is a lot better. Just remember that you will have better production and more expansions.
If the other team is coordinating their bioballs, then you will need to coordinate your baneling/speedling attack. if you mass up a bunch of blings then attack by yourself, while your buddy does the same thing a minutel later, you'll be in trouble. if you hit at the same time, the m + m will have less chance to kill all the blings before the detonate.
You didn't mention what race your teammate plays, but my Zerg friend likes to build Infestors to prevent the endless Terran kiting. If I manage to build fast enough, I'll have psionic storm by the enemy's mid-game push which absolutely rips apart MMM since Fungal Growth prevents them from moving. It also makes it much easier to ambush them with banelings.
I play Terran at Diamond level 2v2 and I would suggest you scout properly. This way you can prevent them from getting very fast expansions. If you see them expand very fast just rush with Zerglings or/and Roaches.
If the Terran takes a fast expand, just expand more (3rd base). The key is to just "defend" until your macro kicks in. Then attack at different locations. As MMM is very slow you can usually pull back before the main force arrives.
This way Terran have to find the right timing. But if your scouting is good enough you will be more than prepared when they move out.
Also burrow 1-2 Banelings at good positions. They are forced to scan this way.