Preheat the oven to 400°F (200°C). Line a sheet pan with parchment or lightly oil a baking dish.
Pat the salmon and sole dry with paper towels. Season both sides with salt and pepper.
Place them on the pan, leaving space between pieces. Put thicker salmon fillets toward the center of the pan and sole toward the edges.
In a small bowl, whisk together olive oil, melted butter, lemon zest, lemon juice, garlic, Dijon, and honey. Stir in the capers.
Spoon the mixture evenly over the fish.
Nestle a few lemon slices on top of each fillet.
Bake for 10–12 minutes, then start checking. Sole cooks fast; it’s done when it flakes easily and turns opaque. Salmon is done when it flakes but still looks slightly translucent in the center, about 125–130°F (52–54°C) if you use a thermometer.
If the sole is done before the salmon, remove it to a plate and tent with foil.
Return the salmon to the oven for 2–4 more minutes, if needed.
Garnish with chopped parsley. Spoon any pan juices over the fish. Serve with steamed vegetables, roasted potatoes, or a simple green salad.