The sequel: I went back to the studio today to record two songs (only got through one) and had decided I wouldn't bring up the mixing issue just yet, But, as he was setting up microphones for me, my engineer said, "What did you think of the mixes?"
I said, "I was quite distressed." I told him a little about my listening process, the notes I took, my opinions. He was totally cool with it -- he said, "Oh, O.K. Well, if you like the raw tracks we'll look at those again and try to keep the mix close to that." Turns out I had misunderstood him -- I thought he was going for final product and he was just giving me somrthing to bounce my opinions off of. Oh. He drew the distinction that I like good performances and that another singer of our mutual acquaintance likes things that sound good on recordings. Ah. Maybe I'll eventually make it to liking performances that also sound good on recordings, but right now I care more about the nuances of the vocals than anything else. He is happy to make mixes that I like better. (I THOUGHT I had completely given up being a drama queen, but I suppose I have more renunciation to do: chalk it up to first-time mixing anxieties).
To clarify a few points: he did the mix with me in the studio and I heard it once there, but he always gives me CDs of what we do to take home, listen to, play for friends, mull over, etc. It was when I heard it at home -- and every time I heard it -- that I had a meltdown.
Crisis averted. And, thanks to everybody here, I learned a few technical definitions and gathered a few resources, I am delighted that the discussion is proving useful to others as well.
Thank you all. I'll revive this thread if need be in future.