Picosecond acoustics has been widely used to study thin film elasticity, hypersound attenuation, and adhesion of thin films to substrates. A major limitation of the technique is its restriction to only longitudinal waves. Although work has been reported on the ultrafast generation and detection of transverse waves, a general method compatible with thin films deposited on silicon is still missing. In this work, we show that by depositing a tilted columnar metal film and using an optical detection sensitive to light polarization, it is possible to excite and detect optically both types of bulk acoustic waves in thin films. The protocol is first established on metalized glass substrates, then applied to a range of transparent films deposited on silicon (silica, AlN, AlScN, and SiC). In each case, Brillouin oscillations are detected at two frequencies, one being the longitudinal mode, the other the transverse. The film thickness and two sound velocities are measured in each thin film. Transverse coherent phonons as high as 116 GHz are observed in the SiC thin film.