Medieval warships were crewed by sailors, but the fighting complement was often simply ordinary infantry from the army, which is why you used to get this 'split' command structure with one set of officers dedicated to sailing the ship (the Master) and one set in command of the soldiers and the fighting part (the Commander/Captain). Sometimes the ships were actually merchant vessels and 'converted' into warships by embarking sailors.

Therefore, you may not even need to have separate marines and crew, you could just bring your regular army (minus the horses) on board your fleet for battle. This separation of the ship from the fighters would also work in reverse, allowing you to have units of marines that can disembark for land operations, rather than remaining stuck to their ships like in most strategy games to date.