No, Divine Sense won't allow you to hit it as if it was visible. Invisibility says that:
Attack rolls against the creature have disadvantage,
and the creature’s attack rolls have advantage.
and Divine Sense does nothing to change that. So what's the advantage of sensing them? Well, the advantage is that you sense them. If you use Divine Sense and discover that you're surrounded by undead and fiends, isn't that better than not knowing?
You could make the argument that if you knew to use Divine Sense, there wouldn't be any point to using it. This isn't really true, though: there's a big difference between knowing that there's something lurking nearby and knowing how many, where, and approximately what creatures are lurking nearby.
Finally, the most important benefit: knowing where it is means that you know where it is. This allows you to use spells like Dispel Magic to remove its invisibility, or just spells like Fireball to hurt it and invisibility be damned. For that matter, you said that you still have disadvantage hitting it, which is true, but at least you can try to hit it. (If you didn't have Divine Sense, you wouldn't even know where it is, you'd just have to swing your sword at a random square and hope. Unless you hit, you won't even know if you guessed right.)