Can posts and pages be mixed?

Or is there some other way of getting what I want? My problem is that I need to have something that looks like a post at the top of my front page, without a date, and the normal blog posts beneath that. It is like a sticky post, but a post with different formatting than the other posts (i.e., no date). I could just write a page, but I don’t know if it is possible to display that on the front page, followed by posts.

Any ideas as to how I can do this?