They do, and have done so since the 1990s. You would know this even if from US TV news if you paid attention. I cannot help but wonder how many people's 'knowledge' of Hezbollah is based on pundits and the occasional movie with random 'terrorists' shouting in Arabic.
They are not part of the regular Lebanese army, but they are a straight up military force. The most obvious parallel I can think of would be the US Marines.
