Step 1 - introduce Stranger A to your friend Alice, when Alice is having a bad day.
Step 2 - introduce Stranger B to your friend Alice, when Alice is having a good day.
Step 3 - ask Strangers A and B to describe Alice's personality. Ding ding ding! They describe different personalities.
But wait, you say, one person's description based on purposely limited evidence is not a complete picture of Alice's personality, the old 3-blind-men-feeling-an-elephant-and-describing-it problem. Indeed this is true. A complete picture of someone's personality would account for the variation in their behaviors, as well as the distribution of those various modes, and anti-depressants could clearly alter that distribution.
If anti-depressants perceptibly alter one's distribution of behavior, I see no reason to say they don't alter one's personality. Of course, it's conceivable someone could feel better internally but not act any different, but that doesn't seem to be what you're saying. You seem to be saying that different behavior != different personality, and I'm asking, well why not?
One could point out that situations affect behavior without affecting personality. If your dog died, you lost your wallet, broke a bone, and your girl-friend broke up with you in the span of a couple weeks, you'd probably be feeling pretty shitty in a way that would affect your behavior. However, this kind of feeling-shitty, unlike with depression, is directly caused by shitty-stimuli and leads to feeling-shitty-behavior. If it were the environmental stimuli of taking anti-depressants that directly lead to more-optimistic-personality-behavior, then I would counter that taking the placebo would provide the exact same environmental stimuli, and hence should lead to the same behavioral changes. However, it doesn't, so I don't think it's unfair to label an anti-depressant as possibly personality-altering.