When Miroku and Sango meet, Miroku restrains himself out of sympathy. Miroku and Sango are constantly getting into fights. However, Miroku once proposed to Sango and Sango accepted. After the proposal, Miroku still flirts with other women, albeit less than before. As the story progresses, it becomes clear that Miroku is falling deeply in love with Sango but since he is unable to come forth with those feelings, he hides it behind inappropriate groping and double entendres. Since Miroku is "technically" a Buddhist priest, Sango usually addresses Miroku with the respectful term houshi-sama (houshi means Buddhist priest, and -sama is a respectful honorific), even when he acts disrespectfully, which is reflected in the dub by dryly calling him "monk".
Despite their "cat and mouse" relationship Sango and Miroku actually make an excellent pair in battle, and whenever the group splits up it's usually split between InuYasha-Kagome and Sango-Miroku. Ironically, with all his groping and innuendo, Miroku doesn't ask Sango to bear his child (as he does with every woman he meets). It is not until she demonstrates jealousy over his asking other women and finally brings the subject to his attention. Surprised, Miroku naturally asked the question, and Sango gave him a typical response.
In episode 118 of the anime series, when Miroku and Sango were battling on Mt. Hakurei, Sango was struck unconscious by Hirakotsu. Miroku then cries out, and picks up Sango and Hiraikotsu while running. Kagura then taunts Miroku, saying that he would have lived a little longer if he had run immediately. Miroku then confesses out loud that Sango is the woman he loves, and he would even sacrifice his very life for her. With that, he opens his Kazaana and sucks in all the yōkai chasing after the pairs.