We realized an integrated microfluidic chip that allows measuring both optical deformability and acoustic compressibility on single cells, by optical stretching and acoustophoresis experiments respectively. Additionally, we propose a measurement protocol that allows evaluating the experimental apparatus parameters before performing the cell-characterization experiments, including a non-destructive method to characterize the optical force distribution inside the microchannel. The chip was used to study important cell-mechanics parameters in two human breast cancer cell lines, MCF7 and MDA-MB231. Results indicate that MDA-MB231 has both higher acoustic compressibility and higher optical deformability than MCF7, but statistical analysis shows that optical deformability and acoustic compressibility are not correlated parameters. This result suggests the possibility to use them to analyze the response of different cellular structures. We also demonstrate that it is possible to perform both measurements on a single cell, and that the order of the two experiments does not affect the retrieved values.