Military Justice Improvement Act of 2019 This bill modifies the process for convening courts-martial for sexual assault cases and certain other offenses. For example, the bill authorizes independent military prosecutors to decide whether to convene courts-martial for (1) sexual assault cases and other specified crimes punishable by confinement of more than one year; and (2) other specified offenses, such as retaliation for reporting a crime, regardless of the maximum punishment authorized for the offenses. Under current law, the military's chain of command generally has sole decisionmaking authority as to whether to prosecute such cases.