Waiver approval is dependent on several factors. One of the factors is how badly that particular military service needs your particular warm body at this particular point in time.
Two of the active duty services are currently overmanned (ie, they have more people on active duty than Congress says they can have). Those two active duty services are the Air Force and the Navy. Because of this, both services are currently getting more applicants for enlistment than they are allowed to take. So, they get to "pick and choose" and only take the * most qualified. *
Too put it bluntly, the Navy (and Air Force) currently have thousands of more applicants each year than they are allowed to accept. Your application requires a criminal history waiver (even if not convicted, you were arrested / charged). Hundreds of other qualified applicants do not require such a waiver. Who do you think the Navy is going to choose?
I should mention here that when it comes to waivers, the military services do not much care either or not it resolved in a conviction. They do not care whether charges were dropped due to some technicality, or due to someone refusing to press charges. They care more about whether or not you actually committed the offense challenged, and not whether you were charged or not due to a legal loophole.
By your own admission, you did commit these two offsets. You were in possession of cocaine, but got out of it because the cop made a "booboo" during the arrest. You committed the offense of domestic battery, but got out of it because your wife refused to press charges. From the military's point of view, you committed these two offsets. Waivers for the Air Force or Navy are both unilaterally.
The Army and Marines are having a harder time recruiting than the Navy and Air Force. While there are no promises, these two services are your best bet.
First of all, the fact that they committed a criminal indemnity will likely require a waiver. Because you use the term "soldier," I assume you're talking about the Army? (Each service has different standards).
"Probation" is considered (by the Army) to be a "civil restraint," because it limits a person's ability to do certain things and / or travel to certain areas without permission. The Army regulation requires at least a 30 day waiting period, following removal from probation before a waiver request can even be processed.
Chances of getting a waiver for the active duty Air Force or active duty Coast Guard are slim. The Air Force is reducing in size, so they are not granting that many waivers (they have a waiting list for those who want to join, so they do not need to approve very many waivers), and one of the Coast Guard's responsibilities is drug enforcement (as you know), so they rarely waiver drug offenses.
If he gets probation, (in most cases), he will not be allowed to join any of the services until his probation is over. There are some exceptions to this.
His chances of getting a waiver (assuming no other offsets) differ, based on the services, and what their current recruiting needs are. In order (easiest to hardest), it would probably be:
Army National Guard, Army Reserves, Active Duty Army, Marine Corps Reserves, Active Duty Marines, Navy Reserves, Active Duty Navy, Coast Guard Reserves, Active Duty Coast Guard, Air Force National Guard, Air Force Reserves, and Active Duty Air Force.