It looks like it only refers to vêtements: http://www.collinsdictionary.com/dictionary/french-english/manteau?showCookiePolicy=true
Of course you mean one "manteau" each... But regarding "leur", it must match the number of the noun. Since "manteaux" is plural, it must be "leurs". You know it is the plural "manteaux" because the verb is plural (sont).
- Leur manteau = their coat
- Leurs manteaux = their coats