In Rock Band 3, only one controller is used for vocals, no matter how many mics are connected. (Also, if you have "All Instruments Mode" on, then no controller is used for vocals.)
If you select Solo, then singing is mostly the same as in Rock Band 1 and 2, with a single track for the vocalist. (While there are differences between older RB tracks and RB3 tracks, the mechanics are the same.)
If you select Harmonies, then singing is the same as in Beatles: Rock Band. One, two, or three vocal tracks will be available, depending on how the song was set up, and the track you match is based on your pitch, not on your microphone. That means the following things are true:
- You can sing both lead and harmony on some tracks, depending on where the harmony comes in. If you are singing in Harmonies mode by yourself, you may need to do this, as some phrases may not have lead vocals. (This also means that on some songs, you can actually get a Double Awesome on some phrases even when you are singing by yourself.)
- On some songs, you may have difficulty on some phrases unless you have someone singing each part. Because RB3 guesses the part you're singing based on pitch, if you do not match the track you intend to sing, it may match you to another part instead, even if you started off the phrase on your intended part. (You can tell this is happening if a pitch arrow starts jumping back and forth between two parts.)
So, in your case, the first controller connected is assumed to be the vocalist's controller, and that person will need to select songs. You can decide between yourselves who will sing each part for each song - if necessary, you can change parts during the song without having to switch mics.