Je traduirais par :

Ils passent tous les deux la nuit ensemble.

I think an easier way to understand the difference between se and ensemble would be with a simpler sentence :

Ces personnes se mangent. AND Ces personnes mangent ensemble.

They would translate respectively to :

These people are eating themselves (or… each other). AND These people are eating together.

Does that help?

Quite often « se » means « self ». So you can think that it stands for object of action:

il         se      laver  ->   he        wash   himself
subject    object  verb        subject   verb   object

Well, the translation is rough, but it’s aimed to be illustrative 😉

Another use of « se » is to express idea of return action, consider this example:

ils s’écrivent -> they write to each other

Also « se » may be used to create passive voice constructions:

il se vend -> il est vendu -> it is sold