I always had the opposite problem. My friend uses Zerg with dreadful efficiency, and I can never beat him with Terran. I can win in ZvZ, but only rarely in TvZ. Granted neither of us are regular players, but it's what happens.
If you play a lot, and want to not let your friend abuse you via RTS, then you'll need to observe his strategies and tendencies, and learn to thwart them. Superior Intelligence is a strength of Zerg, with some Micromanagement: Burrowed units are simple, effective recon and defense in early/mid game. I like burrowing 2-4 zerglings at my opponent's logical expansions (right by the minerals), and pop out when they are about 25% done, kill the SCV, and then the building. You can set them back significantly until they can get scanner sweeps going.
For mid/late game offense, you will NEED Defilers. Dark Cloud right on top of a stack of Goliaths/tanks, and send in upgraded Zerglings. 8 fully-upgraded Zerglings can destroy a stack of Ranged troops within a Dark Cloud, if you can keep them from getting asploded. Add in an Ultralisk or 2 to sponge some damage, and you can even breach a fortified position. Plague is also a killer for Terran army, since they don't have regenerative health; if you get a plague off on a fleet of battlecruisers, tanks, or a defensive bunker, they're easy pickings, even for mutalisks. Enough Defilers can destroy a Terran base without any mulitary support too, since Terran Buildings begin to damage themselves when they're in the red. Plague 2 or 3 clusters of important buildings, and you can sabotauge their tech tree completely.
Second, make sure to use Queens. They're annoying as hell, great as scouts and recon (parasite high-powered units to track their movements and disuade them from using them in combat, and on SCVs to keep tabs on the base (players rarely check their SCVs at old expansions). They can also do crowd control and "cloak scans" with Entangle, and a team of queens can trash a squad of bunkered-in tanks with Spawn Broodling.
Thirdly, learn your land-units, and use your Air primarily for support. Though Air-heavy armies are versatile and powerful, they tend to be expensive and relatively flimsy. A Hydralisks can take a Wraith fairly easily, and 6 can take a battlecruiser, and fewer can with proper support.
I hope that this helps you and your friend work out your problems, so you can get on with your friendship. Good luck in this, sir, and godspeed.