I've always heard that you should take your levothyroxine on an empty stomach (the reason most people take it first thing in the morning) and then wait at least an hour before taking anything else other than water - no food or even other meds. You're supposed to wait four hours before taking supplements - calcium in particular. Since I like to to have a shake for breakfast (high in calcium), I try to wait longer between my levo and my breakfast. I usually wake up in the early morning and then fall back asleep, so I take advantage of this time to take my levo. Then I don't have to wait so long when I get up later.
As for your question… If I understand you correctly, you have two different meds that are supposed to be taken on an empty stomach. I wouldn't take them together. That could cause problems. If you have enough time in the morning, you could stagger them by an hour or so. Another option, if you eat dinner early enough, would be to take one at night before bed and the other in the morning when you wake up. This would be a good question to ask your pharmacist.