Take the wood doors off the cabinets by unscrewing the hinges from the cabinets. Next, unscrew the hinges from the doors as well. Place all hinges and screws in a plastic baggie to keep them safe as you refurbish the cabinets.
Remove any coatings or old stain from the wood doors and the cabinets by going over the doors and cabinets with medium-grit sandpaper. Continue sanding until the wood feels bare and the doors and cabinets have a nearly uniform color.
Fill any holes in the cabinet or the doors with wood filler. Apply the filler with a putty knife, pressing the filler into the holes, and then drag the edge of the putty knife across the filled surface to take off any excess filler.
Go over the doors and cabinets with fine-grit sandpaper once the wood filler dries. Sand until the filled areas sit even with the rest of the door or cabinet's surface, and all the surfaces of the doors and cabinet feel smooth to the touch.
Brush stain over the cabinet and the doors, using a paintbrush. Wait three hours for the stain to dry, and then apply an additional coat of stain if the color does not appear dark enough once it's dry.
Return the doors to the cabinets once the final coat of stain dries. If the hinges appear tarnished, replace the hinges with new ones to help complete the refurbished look.
Remove the doors from the cabinets, and remove the hinges from the doors. Keep the hinges and screws in a baggie together.
Mix epoxy with hardener and apply epoxy to any holes in the doors or cabinet, using the applicator. Skim any excess epoxy off the surface to prevent the epoxy from drying higher than the cabinet or doors.
Apply oil-based primer to the cabinet doors in a thin, even layer. Allow the primer to dry fully, and apply a second coat. Let the second coat dry before you apply paint.
Repaint the composite doors and cabinets with the same color of paint used originally, or use a new paint color to change the look of your bathroom cabinets. Let each coat of paint dry fully, and apply additional coats until the paint is the color that you want.
Brush clear coat over the painted surfaces on the cabinet and doors once the final coat of paint dries. Once the clear coat feels dry to the touch, screw the hinges back onto the doors and return the doors to the cabinet.