[en] Three-dimensional (3D) microwave cavities have been extensively used for coupling and interacting with superconducting quantum bits (qubits), providing a versatile platform for quantum control experiments and for realizing hybrid quantum systems. While having high quality factors (>10"6) superconducting cavities do not permit magnetic field control of qubits. In contrast, cavities made of normal metals are transparent to magnetic fields, but experience lower quality factors (∝10"4). We have created a hybrid cavity which is primarily composed of aluminium but also contains a small copper insert reaching the internal quality factor of ≅10"5, an order of magnitude improvement over all previously tested normal metal cavities. In order to demonstrate precise magnetic control, we performed spectroscopy of three superconducting qubits, where individual control of each qubit's frequency was exerted with small external wire coils. An improvement in quality factor and magnetic field control makes this 3D hybrid cavity an attractive new element for circuit quantum electrodynamics experiments. (orig.)