Does the block count as one of our three hits?

Yes. This is one of the biggest differences from indoor volleyball. In beach volleyball, a blocking contact counts as a team hit (Rule 14.4). After a block touch, your team has only two more hits to return the ball.

The first hit after the block may be made by either player, including the one who touched the ball in the block.

Other block rules (Rule 14):

• Blocking is reaching above the top of the net to intercept the ball coming from the opponent. A block is completed whenever a blocker touches the ball. A collective block is two players blocking close together.
• Quick, continuous contacts by one or both blockers during one action are allowed.
• You may reach over the net to block, as long as you don't interfere with the opponent's play before their attack hit.
• Blocking a serve is forbidden.
• Faults also include touching the ball in the opponent's space before their attack hit, blocking in the opponent's space from outside the antenna, and the ball going out off the block.