Preheat the oven to 350°F. Butter a 9x9-inch baking pan and set aside.
For fruit: Mix the peaches, raspberries, honey, and lemon juice in a large bowl. Add the flour and mix lightly. Turn the ingredients into the prepared pan. Set aside.
For topping: Combine the flour, oats, oat bran, brown sugar, cinnamon, and salt in a large bowl. Add the butter and rub it in with your fingers until you have uniform, gravel-like crumbs. (This can also be done in the food processor. Pulse until you have uniform crumbs; don’t let the mixture turn clumpy.) Spread the mixture evenly over the fruit and bake for about 40 minutes, until the top is golden brown and the juices bubble thickly. Cool on a rack for at least 15 minutes before serving.