All of the branches work together during operations and joint missions in Unified Combatant Commands, under the authority of the Secretary of Defense with the typical exception of the Coast Guard. Each of the Unified Combatant Commands is headed by a Combatant Commander, a senior commissioned officer who exercises supreme command authority per 10 U.S.C. § 164 over all of the forces, regardless of branch, within his geographical or functional command. By statute, the chain of command flows from the President to the Secretary of Defense to each of the Combatant Commanders. In practice, the Chairman of the Joint Chiefs of Staff often acts as an intermediary between the Secretary of Defense and the Combatant Commanders.
When you are considered a career in the military you need to take the ASVAB test. But each branch of the military has different ASVAB requirements that you need to meet. They are different levels of education that you must reach to take the test. But you also need to score a certain amount of points on that ASVAB test to gain access into the branch you desire.