Time-resolved optical spectroscopy (TR-OS) has emerged as a fundamental spectroscopic tool for probing complex materials, to both investigate ground-state-related properties and trigger phase transitions among different states with peculiar electronic and lattice structures. We describe a versatile approach to perform polarization-resolved TR-OS measurements, by combining broadband detection with the capability to simultaneously probe two orthogonal polarization states. This method allows us to probe, with femtoseconds resolution, the frequency-resolved reflectivity or transmittivity variations along two mutually orthogonal directions, matching the principal axis of the crystal structure of the material under scrutiny. We report on the results obtained by acquiring the polarization-dependent transient reflectivity of two polytypes of the MoTe₂ compound, with 2H and 1T’ crystal structures. We reveal marked anisotropies in the time-resolved reflectivity signal of 1T’-MoTe₂, which are connected to the crystal structure of the compound. Polarization- and time- resolved spectroscopic measurements can thus provide information about the nature and dynamics of both the electronic and crystal lattice subsystems, advancing the comprehension of their inter-dependence, in particular in the case of photoinduced phase transitions; in addition, they provide a broadband measurement of transient polarization rotations.