The official rulings on this have gone back and forth, but the current rule from the designer is that Militia causes you to discard one at a time, and thus your opponent would get to see all cards being discarded.
This has been a topic of discussion both at BGG and the Dominion Strategy Forums multiple times. Most recently the discussion has come up in regards with how to handle discarding Village Green (which lets you play it when you discard it), but the same discussion would affect whether your opponents are allowed to see all cards that have been discarded.
The most recent statement by Donald X I have been able to find is from November 2020, in which he says:
I still tentatively plan to change [Militia causes you to discard one at a time] to, discard all at once, then do the Village Greens.
Emphasis mine; he was considering making a rule change to discard all at once, but no decision had been made. In January 2021, in regards to whether he had made a decision, he stated:
It's not on my mind. I have no game night currently, etc.
In a BGG thread from 2016, Donald first stated
You discard the cards all at once, with only the ends-up-on-top card revealed
as the other answer quotes. However, shortly after in the same thread (2 months later), he corrected that:
Yes, sorry; Inn is "discard 2 cards at once" while Militia is "repeatedly discard 1 card until at 3."
In a 2014 thread on the Dominion Strategy Forums, Donald X discussed both interpretations:
Minion is "discards his hand." Militia is "discards down to 3 cards in hand." The question is, how does the process of "discard down to 3" work - it's specific to that phrasing. It seems to me like you keep discarding until you have 3. Tunnel could interrupt that because it does something when discarded.
It may feel like Militia is "calculate the number of cards in your hand minus 3, and if it's greater than zero, discard that many." It doesn't say that though.
As always very few people will see any ruling I make on this, and if I'm not contradicting a rulebook I would tend to like things to work how people who didn't think about it would play them. Maybe everyone is subtracting 3; it's hard to say.
Another slightly more recent ruling from Donald X:
Oh I see. I don't know what the online version does there either, but yes. One at a time for both [Monastery and Militia], except, maybe the interface can be friendlier for typical no-such-weirdness cases.
Finally, a couple threads with more discussion and information, but no other specific rulings to quote: