IF it's propelled, it's no longer a push mower. Walk behind would be more descriptive.

I doubt you'll find any kind of "residential" walk behind with reverse since some people would be cutting their feet off.
Just too much of a liability.

Well, there's a 4WD, but still no reverse. If you think about it, would you really want a power mower in reverse coming back at your feet? :)

Thank you for the two responses, both of which make a lot of sense regarding the danger of injury. My problem is that my Wife likes to help with mowing my four acres of grass. I use a zero-turn and she uses a regular riding mower. We need to use a push mower sometimes and it is too difficult for her to pull backwards when necessary. Is there a mower which completely disengages the forward drive assist or is the drive assist adjustable to almost completely release the forward assist?

I'm not aware of any walk behinds that you can't disengage the drive.
Else the mower would be moving forward when you were starting the engine.

I think it is only the front wheel drive models that don't disengage the wheels, as it assumes you will be tilting the mower back to make a turn. All the rear-wheel drive models disengage when you release the drive bail.

Both Snapper and Toro can be pulled backwards. On one, just release your thumb and on the Toro, just stop pushing the bar. Both are rear wheel drive.

You should buy only a rear wheel drive mower.
On mowers with a drive bar (bail) that you pull up and hold against the bar to drive, as soon as you release the bail it completely disengages. The Toro version is called 'Variable Speed' as you can 'feather' the bail for assist at slower speeds. This is the kind I recommend. The Toro 'Personal Pace' can be tricky to disengage on the pull-back because it has no operating lever. The belt is tightened by a sliding handle as you push the mower forward. So, the drive won't release until the handle rises all the way up by spring action and the wheels coast forward a short distance. The Toro drive is also the simplest and longest-lasting. The 'Variable Speed' and personal Pace' are both variations of the same design with a belt that is designed to constantly slip. Even so, the belts last a very long time - I have been using two mowers with 'Variable Speed' for years with no belt failure. They have adjustments to compensate for stretch/wear.
Toro sells a 20" mower under the Lawn-Boy brand that is inexpensive and has 'Variable Speed'. You find these in Home Centers and they are highly-rated by users. I recommended one to my son and he really likes it. It's a light, maneuverable mower for trim work or smaller yards. Notice the overhead valve engine on the linked mower.

Here is a link that might be useful: LB 10632

I wish there were a 21" self propelled mower that had reverse as well. It would make forward and backward trimming around things much less tiresome.

Sarlo, and some others, make a "high wheel" mower, where a tiny wheel or gear presses directly against the wheels to drive them. When it is released the rear wheels are completely free to "free wheel" without a belt or the transmission trying to fight you. The large wheels also roll over rough ground nicely. The mowers only have one speed though. They are also designed as rough duty mowers and don't have as much cutting height adjustability as regular residential mowers do.

Another option are the friction plate drive systems like the old Snappers and Ariens mowers have. When the disc lifts free of the drive plate the engine is completely disconnected from the transmission. Pulling them backwards still turns part of the transmission but not as bad as fighting a badly functioning belt drive transmission. I don't know about current snapper rear wheel drive mowers, but Ariens only uses the friction plate transmission on their "classic" line of mowers these days.

I only learned this year that it is not due to the transmission that mowers want to resist disengaging or freely rolling backwards. There is a special type of washer on the axle by the wheels that is supposed to grab when going forward but not grab when rolling in reverse. They may be plastic and wear out. I read that is why Toro, until recently, always had the grease zerks on the back wheels - to help keep those functioning.

My 36" commercial walk behind has a simple safe reverse on it. Its called "operator assisted" reverse. You shift into reverse, but then have to give it a light tug before it rolls back. I don't know how the Peerless transmission accomplishes that, but it's like its asking you, for safety sake, if you are sure you want the mower to back up and the tug confirms it and the mower starts backing up.