Material-based two-level systems (TLSs), appearing as defects in low-temperature devices including superconducting qubits and photon detectors, are difficult to characterize. In this study we apply a uniform dc electric field across a film to tune the energies of TLSs within. The film is embedded in a superconducting resonator such that it forms a circuit quantum electrodynamical system. The energy of individual TLSs is observed as a function of the known tuning field. By studying TLSs for which we can determine the tunneling energy, the actual p(z), dipole moments projected along the uniform field direction, are individually obtained. A distribution is created with 60 pz. We describe the distribution using a model with two dipole moment magnitudes, and a fit yields the corresponding values p = p(1) = 2.8 +/- 0.2 D and p = p(2) = 8.3 +/- 0.4 D. For a strong-coupled TLS the vacuum-Rabi splitting can be obtained with pz and tunneling energy. This allows a measurement of the circuit s zero-point electric-field fluctuations, in a method that does not need the electric-field volume.