Terran vs Zerg can be a hard matchup to play against since Mutalisks are so powerful against Terran. If you use this strategy then you won’t have to worry much about Mutalisks, you’ll be doing air harassment of your own.
Start your base off by walling in with a Barracks and getting a fast Factory. Make a few Hellions and go harass the Zerg mineral line to slow down his income and teching ability. Then add a Tech Lab onto your Starport, research cloak and make some Banshees. Do as much mineral harassment as possible with your Banshees; kill Queens, Drones and key structures if you can.
After making a couple Banshees and doing some income harassment make another Starport (w/ Reactor) and start making a lot of Vikings. Once you have around 12 Vikings move out and start killing Zerg Overlords. If you see a Queen or 2 all alone, land your Vikings and take it out.
Use your Vikings to control air and keep up the harassment. Land behind the Zerg mineral patches to take out Drones. When ground units come take off and move to an expansion to do the same. When you establish map control, keep expanding and adding on Starports. Make two Armories as well to start upgrading your air weapons and armor.
Once your income gets real strong throw down a Fusion Core and start making Battlecruisers. Battlecruisers are very strong against ground units. If Zerg goes for mass Hydralisks upgrade your Hellions with the blue-flame upgrade and make a lot of them. They will roast through Hydras very quick while they focus on your Battlecruisers.