They have spirits, not souls.
Let's go for a ride down a rabbit hole of European Christian fanon you probably didn't know existed.
Demons aren't biological
This one's just good theology from any perspective. Hell isn't a physical place that sits adjacent to the Earth's mantle. Hell is a state of being, and its native denizens are demons. Demons are angels by creation. Angels and demons are both eternal creatures, like God. They exist outside of time and have free will of their own. As eternal creatures, they saw and understood the Fall and Salvation from the dawn of time. In that timeless moment, they had a choice: "Serviam" or "Non serviam." I will serve, or I will not serve. The "serve" here is literally God, but the proposed hanging point is actually serving man. Because the angels won't participate in Salvation, but God will become incarnate as a man, the angels will ultimately be serving humans. Compared to angels, humans are weak in both will and body, limited in perception and wisdom, and frankly not cut out to tie Michael's sandals. And they're being asked to serve those things. Gross.
According to popular interpretations of Revelation 12:4, about a third of the angels were convinced to say no by Satan, and they wage war against the angels. This "war" isn't with blood and swords. That part's just analogy. Instead, they're fighting to bring about what the demons see as the proper natural order. They're fighting over the plan of Salvation, timelessly, as equal beings of equal free will.
Spirits don't create
Creation in the eternal time posture is an ability that only belongs to God. Spirits, angelic or demonic, have no creative abilities of their own. They can rearrange bits of matter like a smith crafts a sword, but they can't make new things.
Humans aren't spiritual beings, though. Humans have souls. Souls aren't eternal, contrary to some sloppy pseudotheological expressions to the contrary. They are created in time, exist in time, express their will in time, through some thoroughly handwaved interplay between God and man. Souls can give rise to new souls. We call this birth. It's entirely natural for souls to do this. Despite being as immaterial as spirits, they're really not related material at all.
Demons have an agenda
So, back to that war. The most common interpretation of the war is that the demons are fighting to stymie Salvation in general, to prove that they knew better than God all along. In my mind, an equally plausible explanation (and much better one for your story) is that the demons just want proper order. They're angels, after all. They like things to be a certain way, ordered according to cosmic spiritual principles and hierarchies. Mainly, they want humans to assume their proper place as subservient to angels and demons. The Salvation of man is pretty much irrelevant to them. Now, serving a demon instead of God means you're in a state of mortal sin and you're rejecting Salvation and you're going to Hell, but you made friends there, so this might not be the worst thing ever. You're a slave, but better a loyal slave than a rebellious slave when you're spending the latter half of eternity with control freaks.
They aren't particularly out to harm their loyal servants. Party with them once a generation? Sure. Pleasure is a good thing, and humans are meant to orient themselves towards the good. Grant them power? You betcha, because humans who orient themselves towards their proper end should have a place in the mortal hierarchy above the ones who don't. Have babies with them? Uhhhh...sure? It's going to get handwavy here. Maybe these cambions/nephilim are seen as an appropriate intermediary between the demons and the humans, because...
Cambions are their demonic parent, spiritually speaking
They're not animated by a soul, because it takes two souls to do that. They're not drawing their free will from a soul. They get it from a spirit made permanently manifest by hijacking the biology behind human birth. There's no reason to believe this would harm the demon any. Spirits are eternal and indivisible. You don't really get "more" or "less" of a spirit by having it incarnate. This is pretty much a great deal for a demon. Spirits don't fail to do what they intend, limits of physical incarnation aside. They don't have doubt. They're going to be oriented towards the goals of the parent, at least to the limits of their perception of them (and you could play this to any degree - there's no reason for them to be able to access demonic perspective, or not to be able to, or pretty much anywhere in between). They're also natural lieutenants of the demons in the temporal order. The demons would totally do this if the humans agreed to place the cambions/nephilim above themselves in their hierarchy.
You can soften it and say they're a mingling of the soul of the human parent and the spirit of the demon, but I say fuck it, go all in.