What is the grammar of the word married in this sentence?
They are getting married in April.
The ‘Cambridge Grammar of English’ by Carter and McCarthy calls this construction the get-passive. That perhaps becomes clearer if we re-write the sentence as They will be married in April. Married is the past participle of the verb marry, just as it is in the more conventional passive. As the authors say, 'the get-passive is used in more informal contexts and is more common in spoken than in written English.’
It's a past participle used as an adjective. So it's an adjective. The problem is the action and process involved in this word as it means that an act is going to happen.