I warned that the previous post was provisional, and I believe I've cleaned up my thinking about whether there's a kind of pride that cuts across, rather than being in direct opposition with, humility. The short answer is that I think there is such pride, as with the "proud man" who, though he might be hungry, refuses to accept a handout. What Tara Smith seems to emphasize in such cases as pride we might just as well call a kind of commitment to certain (perhaps especially moral) principles. This seems rather different from the "pride" of the arrogant person, insofar as the arrogant person has an elevated (or over-inflated) view of himself, while the "proud man" above, if anything, has an elevated view of his principles. That is, he puts his principles above his own (mere) self-interest, as well as above "compromising" actions that would require him to break with his principles.
Here's how I would now illustrate the idea that pride in this sense intersects with humility (again, click to enlarge):
This also allows us to explain two different senses of being "too proud": one can be too proud in the sense of being arrogant, vain, or conceited, but one can also be too proud in being overly dogmatic or zealous in one's commitments. (Compare this to what Bernard Gert means by "moral arrogance.") We might suggest that the man who refuses a handout when his children are starving is being "too proud" in that sense.
This analysis still leaves open whether there is anything at stake in calling the virtue along the self-regard axis "humility" or "proper pride," or whether those are simply synonymous terms. As I mentioned before, I think a humble person can "take pride in" certain achievements and so forth. One might say that a humble person just doesn't let it "go to his head." But we might say the same thing about the person who shows "proper pride."
Perhaps part of the issue here depends upon where a person is at: someone tending toward too little self-regard, in ways that are debilitating, might need to be encouraged to take pride in some aspects of himself, or at least be brought to see the how self-respect is possible (even if one lacks anything in particular to be proud of). This seems particularly true where a person or group has been subjected to injustice and oppression (and thereby humialation). On the other hand, where someone is tending toward arrogance or vanity, it makes sense to emphasize humility.
We could then see critics of humility, such as Nietzsche and Hume, as rejecting in particular the severe form of Christian humility (rooted in medieval views) because they see these views as tending toward "too much" humility, viz. undue self-deprecation and servility.
On the other hand, in the midst of identity politics, partisanship, and various ideological clashes which threaten or encourage or involve violence against the "other," it strikes me that humility, particularly epistemic humility, is a highly desirable trait. What I'm working on is how to make out the praiseworthiness of such humility in a way that doesn't entail that we should let go of our own deep convictions. (That is, one might worry that aspiring to such humility would lead to some amount of alienation, where our own deep commitments involve matters of significant controversy.) More on that another time.