Dealing with cloaked banshees as any race on any map
Lets make it more generic, I'll leave the references to TvT in it, but I'm going to expand this answer to 'dealing with cloaked banshees as any race on any map'
Your Build
First off, a 1-1-1 as Terran is an excellent way to defend the banshee rush. The best builds with all races are the ones that can defend you against the most variations of attacks. Chances are you wont be able to scout the banshees before you have to commit to a build (like a 1-1-1 or hatch on 15). Stick with what you are most comfortable with in terms of build, then determine how best to defend with that build (all Terran builds can defend banshees with the exception of maurader heavy).
The Defense
Someone who commits to 2-3 banshees with cloak and doesn't do sufficient damage is punished enough. In terms of a pro-game, it is almost a GG to make that type of commitment and not win or cripple the opponent. This is called an all-in. The fact of the matter is that any of your solutions (as long as you live) will punish him! He is making a significant investment and you surviving with minimum loses puts him behind.
Relying solely on static defense like 2 turrets, cannons, or spore crawlers: You defend against cloak but will have a hard time killing the banshees. You need an army to deal with the mobility of the banshees. Killing the banshees is key, chances are he has maybe ~6 marines + 2-3 banshees as the entire extent of his army. If you throw down two turrets you will be able to detect him and prevent damage to your worker line, but chances are his banshees will escape alive and be repaired. You don't want them coming back...
A proper defense of banshees with cloak is minimum detection (maybe 1-2 turrets max for any race, or a cloak detection unit like the overseerer or observer) and the ability to kill the banshees. You can do this with most ranged units if you know the banshees are coming:
either stim marines and/or vikings as Terran.
Lots of queens with transfuse, mutalisks, or hydras as Zerg.
Stalkers and sentries as Protoss.
It is important to note that a scan or a static defense to kill his banshees isn't the end of the world as they are such a commitment on his part. Just make sure you kill them.
The Follow Up
How you follow up is up to you.
Macro
If you are confident in your macro play you have already put him behind by surviving his attack. You can put him even more behind by expanding. Good players recognize that going for the instant kill is often a high risk situation, the way to exploit an advantage in starcraft is to get 'more ahead'. Advantages build exponentially in Starcraft 2. You can safely expand knowing he has a smaller army then you due to his commitment to high tech. This lets you grow a larger economy earlier leading to an even larger army later. This is especially true with Zerg as their economic advantage can painfully punish mistakes like this from Terran later in the game. I will pick this solution every time. A definite win in ten minutes is better then a 90% chance to win now.
Micro
If you think your opponent is better in a long term macro game then you, you can attempt a counter attack immediately after you kill his banshees. This has a much higher risk to losing your advantage and could leave you on equal footings with him (or worse!). There are variations to the extent you counter attack though, you could probe (which is always good) and if he looks weak enough throw into an all-in with scv's and hope for a win or you can simply probe, back off and choose the macro alternative.
