If I had it figured out formally, I’d direct you to my monograph!
The side-by-side nature of Christianity is illustrated best in the two natures of Christ. Christ being fully man and fully God is an incomprehensible, yet real, mix of the natural and supernatural. The natures are literally side-by-side in some paradoxical fashion (NOT like two boards glued together). If you want to dive a little deeper into Lutheranism, this is also illustrated in the sacraments of baptism and communion. We take the natural world very seriously, to the point of the natural world (wedded to the word of God) being a vehicle of forgiveness of sins.
Philosophically, I would say that my naturalism is an epistemic naturalism. I think that philosophy IS different from the sciences by degree NOT kind. This means that when trying to figure out how to know the world, one should employ the tools of psychology, biology, sociology, etc. However, this means that metaphysically, a lot is left open to argument and disagreement. I am okay with the uncertainty that follows from not having metaphysical closure.
Many of my brethren think that God provides closure to metaphysics or somehow significantly reorients my cognitive faculties to see the world differently. The problem is, that we, once redeemed, employ the same cognitive faculties as those who are lost. We go to the same eye doctors and dentists when our faculties fail. Even if God somehow provides closure to the metaphysical speculation, I speculate using my perfectly natural faculties. What has changed is something in my larger outlook on life. One begins to see the value in the Wisdom literature of the OT – There really isn’t anything new under the sun or Son – thus, I am free to live life according to the gifts God gave me. This might mean being an evolutionary biologist, or a pastor, or a mechanic, or a stay-at-home mom, or a teacher, or a chemist (@Jordan!), or God forbid, a philosopher!
I believe in God due to the resurrection, this happened in space-time, including a reversal of cellular respiration. Without Christ, God is meaningless – thus, I see myself as much more of a naturalist. I do believe in the supernatural, but it is only because my natural epistemic faculties had to deal with a world in which a dead man seems to be raised, walking and eating with friends and enemies.