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We study a planar Josephson junction under an applied DC voltage bias in the presence of an in-plane magnetic field. Upon tuning the bias voltage across the junction V_{J}, the two ends of the junction are shown to simultaneously host both zero and π Majorana modes. These modes can be probed using either a scanning-tunneling-microscopy measurement or through resonant Andreev tunneling from a lead coupled to the junction. While these modes are mostly bound to the junction's ends, they can hybridize with the bulk by absorbing or emitting photons. We analyze this process both numerically and analytically, demonstrating that it can become negligible under typical experimental conditions. Transport signatures of the zero and π Majorana states are shown to be robust to moderate disorder.