You may be thinking of the George Lucas produced "Twice Upon a Time." It used very simple animation, though not just black and white. The tall, mute man was a Charlie Chaplin-type character called Mumsford (or Mums), and the talking dog was Ralph, the all-purpose wonder animal. Here's the link
to the synopsis on IMDB. The military wasn't really a military; it was the leader of the Murk, Synonamess Botch, who, along with his nightmare buzzard army, wanted to stop time, plant nightmare bombs all over the world, and then start time up again and detonate the bombs, thereby plunging the world into one huge nightmare.
I absolutely love this movie, but there is not now and likely will never be a DVD release (it is available on VHS). The directors have a long-standing feud over which version to release; there was apparently a "dirty" version that was shown on HBO once or twice, and a "clean" version that was released on video and to other outlets. Each director backs his version, and this battle has basically buried a wonderfully entertaining film and relegated it to obscurity. I've mentioned it here a couple of times, but I seem to be the only one among the members here who has ever seen it, or at least the only one with any interest in it.
Hope this helps.