I would highly recommend reading the Superman/Batman series. I think there are 7 of them currently. They are incredibly good at portraying the relationship between the two men, both Batman/Superman and Bruce/Clark. They show the thoughts of each man, which although running along very similar lines, definitely show that they are two sides of the same coin (i.e. Bruce: In a very short time with no one hurt, everything is solved; Clark: A long hour later with thousands of people terrified out of their minds, the nightmare is ended. Or something along those lines).
If you go by these, which I believe are newer comic books, Thomas Wayne and his wife were driving through Kansas for some reason or another (I can't recall exactly why), when they saw a meteorite land nearby. Thomas, being a curious man, touched it and his consciousness was transported to Krypton, where Jor-El spoke to him to find out if Earth was a good place to send his son. Because Thomas's wife (whose name is also Martha, curiously enough) is pregnant at the time with Bruce, Thomas is able to give good answers to Jor-El, namely telling him that if he were to find a baby, regardless of if it were in a spaceship or not, he would treat it as his own. Therefore, Jor-El decides Earth is the place to send Kal-El.
When Thomas returns to Earth (only seconds of his time after his departure), he takes the communication device and begins developing its technology and patenting it, which is where he got all the money Bruce inherited.
Discovering this really goes a long way in developing Clark and Bruce's relationship.
I don't know if that helps or not, but I really enjoyed the books even though before them I wasn't a Batman fan. I don't recall that they reveal how they discovered each other's identity (although it is brought out that Bruce is careful to line his cowls with lead), but it does touch on the different aspects of him in regards to Clark/Superman.
And though I believe someone else already said this, it is a huge point that Batman does NOT kill anyone. In fact, he goes to great lengths to make sure that he doesn't ever end anyone's life.
Hope it helps
--from another L&C fan just discovering bits of Batman.
