On the contrary, it appears that the news caused Heathcliff to greatly clarify what he wanted to do. There is no sense that he became mad or insane. Actually, if we look at what he tells Catherine in Chapter Ten, when he returns to the Yorkshire Moors after his time away, he seemed to have been quite decided about what he would do when he heard of her marriage to Edgar Linton:
I heard of your marriage, Cathy, not long since; and, while waiting in the yard below, I meditated this plan--just to have one glimpse of your face, a stare of surprise, perhaps, and pretended pleasure; afterwards settle my score with Hindley; and then prevent the law by doing execution on myself.
His plan is definitely extreme, but delivered in a reasonable voice. Having lost his one true love, there appears no other option for Heathcliff than to settle his scores and end his own life. Of course, the warmth of the greeting that he receives from Catherine changes his plan and gives him hope. So, Heathcliff does not react to the news of Catherine's marriage to Edgar with madness. Of course, he is upset, but he manages to control his emotions and responds in a way that is extreme but reasonable given the extent of his devotion and love towards her.