detectors that simultaneously achieve high efficiency, low dark counts, and continuous operation has proved challenging. Existing detectors operate cyclically, forcing a trade-off between efficiency and duty cycle. Here, we demonstrate a continuously operated microwave single-photon detector based on a superconducting artificial molecule. In our scheme, an incoming photon is captured by a bright state of the molecule and then transferred to a long-lived dark state via a driven-dissipative process. Photon „clicks“ are revealed as quantum jumps in the continuously monitored dark state. We observe a cyclic detection efficiency of 0.73, and a continuous detection efficiency of 0.47 over a 5MHz instantaneous bandwidth, with a 1μs temporal resolution and a 15μs dead time. By overcoming the trade-off between efficiency and duty cycle, this approach establishes continuous microwave photon detection for quantum sensing, quantum thermodynamics, and fundamental physics.