  We study Landau-Zener-Stueckelberg-Majorana (LZSM) interferometry under the
influence of projective readout using a charge qubit tunnel-coupled to a
fermionic sea. This allows us to characterise the coherent charge qubit
dynamics in the strong-driving regime. The device is realised within a silicon
complementary metal-oxide-semiconductor (CMOS) transistor. We first read out
the charge state of the system in a continuous non-demolition manner by
measuring the dispersive response of a high-frequency electrical resonator
coupled to the quantum system via the gate. By performing multiple fast
passages around the qubit avoided crossing, we observe a multi-passage LZSM
interferometry pattern. At larger driving amplitudes, a projective measurement
to an even-parity charge state is realised, showing a strong enhancement of the
dispersive readout signal. At even larger driving amplitudes, two projective
measurements are realised within the coherent evolution resulting in the
disappearance of the interference pattern. Our results demonstrate a way to
increase the state readout signal of coherent quantum systems and replicate
single-electron analogues of optical interferometry within a CMOS transistor.
