This paper describes a new microfluidic biosensor with capabilities of studying single cell biophysical properties. The chip contains four parallel sensing channels, where each channel includes two constriction regions separated by a relaxation region. All channels share a pair of electrodes to record the electrical impedance. Single cell impedance magnitudes and phases at different frequencies were obtained. The deformation and transition time information of cells passing through two sequential constriction regions were gained from the time points on impedance magnitude variations. Constriction channels separated by relaxation regions have been proven to improve the sensitivity of distinguishing single cells. The relaxation region between two sequential constriction channels provides extra time stamps that can be identified in the impedance plots. The new chip allows simultaneous measurement of the biophysical attributes of multiple cells in different channels, thereby increasing the overall throughput of the chip. Using the biomechanical parameters represented by the time stamps in the impedance results, breast cancer cells (MDA-MB-231) and the normal epithelial cells (MCF-10A) could be distinguished by 85%. The prediction accuracy at the single-cell level reached 97% when both biomechanical and bioelectrical parameters were utilized. While the new label-free assay has been tested to distinguish between normal and cancer cells, its application can be extended to include cell-drug interactions and circulating tumor cell detection in blood.