I once read that although there are many different types of love (romantic, parent/child, etc.), the two things every kind of love has (if it's right) is respect for, and admiration of, the other person.
I'd think that if you don't like someone there are some things about them, or that they do, that you don't respect and/or admire; so based on that, I don't think you can really love someone you don't like.
I do think, though, you can really love someone whose behavior you don't like. Also, I know you can love someone but be angry at them and therefore feel (for the moment) as if you don't like them.
We often hear parents say they "love but don't like" their child. In fact, some parents actually tell their child that. I really think such parents need to sort out whether it's their child's behavior they aren't happy with, or whether they're angry with the child for the moment; and stop using that particular phrase/sentence to inaccurately describe their temporarily ambivalent feelings toward their child. OR, if they can't truly feel they both love and like the person that their child is, they should at least try to act as if they do (or maybe even consider finding someone who would make a more loving parent to that child).
I think in most parents' cases, this is just a careless and inadequately thought-out thing they say (maybe because they've heard others say it), and they just need someone to point out those differences between not liking behavior, being angry with, and actually disliking the person himself.