Good afternoon Hisham
The one who wrote the sentence actually used the future perfect continuous. It's form is:
Subject + auxiliary will + auxiliary have + auxiliary be + main verb
we will have been married
The reason why he did this is because the future perfect continuous looks at the past from the future. Its duration is measure at a time in the future for a thing that happened in the past and is continuous up until the set point in the future. Hence why he said "By next month, we will have been married for 20 years.".
'By next month' is the duration in the future that is used to measure the time. "we will have been married for 20 years" is the time in the past up until the time in the future that was used to measure the event.
He used the correct tense because he is talking about a single event. So therefore, he used the future perfect continuous tense.
We use the future perfect tense when we are talking about two different actions.A completed future action before a 2nd action. (The second action is in the present simple form.)
For example:
I will have finished my homework by the time mom arrives.
As you can see the first action (I will have finished my homework) is completed before the second action (by the time mom arrives.)
I hope this helps and clarifies when we use the future perfect tense and when we use the future perfect continuous tense.