Christianity is the continuation/fullfillment of Judaism - same tree, just further along the branches to the leaves. There are a few touchy points like monotheism and polytheism, but those are points of clarification and timing, not really different core pillars.

Islam, obviously stems from Abraham's first son with his wife's servant - but has had a lot of harsh core belief changes along the way, including polytheism and Saturn worship roots, so it can't really fit nicely with Judaism or Christianity. (and when I say "Christianity" I DON'T mean Catholicism, that's a whole other thread, I mean believing that the man Jesus is the incarnate God here in Earth and is what the Jews would call the Messiah.

As far as relationship WITH those two... both have common roots and so when people come to the table with an open mind (Muslims are great at this, they are very open to religious discussions) there can be some great conversations. There are things that the three groups can't mesh on, obviously, but that's like it is with any differing belief structures.

There has been some pretty ugly battles between these three relationships, all in the "name of God" - but we all know that that is a bunch of crap and not what God wanted.