Both my wife and receive monthly checks from our company retirement plans. I don't understand how the RMD applies to this distribution.

If this is a company pension plan that terminates on your passing, it is not subject to RMD. The IRS wants to get their cut, but a pension has no value after you pass.  (There are options to pass it on to your spouse.)

If it is simply a retirement distribution (from a 401K or IRA) that you happen to take monthly distributions from, you will have to be aware of your RMD obligation.  This can be determined at the beginning of each year, and monthly distributions can be made.

To clarify somewhat....for the 1099-R you receive from a company pension (not a 401k or IRA), the tax software will asks if it is an RMD once you have reached age 72  (used to be 70.5).   For that pension 1099-R, you just answer yes....it is an RMD, and ALL of it was an RMD.   

The tax software has no way of knowing if the 1099-R was a regular pension that produced the 1099-R, or whether it was (say) a 401k, where you do have to be careful to initiate/take the proper RMD $$ every year yourself.