I agree with Elizabeth that the easiest approach is cold turkey, and that if there is a way to get DH on board with tossing the box, that would be the way to go. If that's impossible, try putting the tv(s) away and asking DH to support your efforts by not turning on the tv when the children are awake.
As far as the kids go, the first week might be tough, but I think you'd be surprised at how soon they adjust to the new no-tv norm.
I have 3 boys and one very active girl. My secret to sanity: I keep them moving, and we spend a lot of time engaged in physical activites--swimming (lessons, beach time, and free swim at the local pool), basketball, biking. The three oldest play soccer and two do dance. They also take piano, and that requires a good bit of practice time. Some might think they are a little overscheduled, but lots of their activites are open ended and fun--for example, I plant my beach chair, hand out the buckets, shovels and boogie boards and relax (sort of) while they do their own things for hours at a time. But still, since they don't watch any tv and watched exactly one movie all summer they have plenty of time to play tag in the yard or collect daisies or read or draw.
Sorry for the novel. The bottom line is not having the box or at least not giving the kids access to the box is a big first step. You'll find your own new way of keeping them engaged and busy very quickly.
I'll warn you of one thing: once you give it up for a while, you never want to go back. In fact, I think that once you reach the point where you are now--sick of the thing and painfully aware the box's costs--you won't really be happy until you do wean the kids (and yourself, if you watch any) off it. You're just too aware now to not go forward!
Also, you're house will get messier (and louder) but the kids will have time to help more!