Analysis of fetal electrocardiogram (f- ECG) waveforms, as well as fetal heart-rate (fHR) evaluation, provide important information about the condition of the fetus during pregnancy. A continuous monitoring of f-ECG, for example using the technologies already applied for adults ECG tele-monitoring (e.g., Wireless Body Sensor Networks, WBSNs), may increase early detection of fetal arrhythmias. In this work, we propose a novel framework, based on Compressive Sensing (CS) theory, for the compression and joint detection/classification of mother and fetal heart beats.