Multi-static cooperative sensing emerges as a promising technology for advancing integrated sensing and communication (ISAC), enhancing sensing accuracy and range. In this paper, we develop a unified design framework for joint active and passive sensing (JAPS). In particular, we consider a JAPSbased cooperative multi-static ISAC system for coexisting downlink (DL) and uplink (UL) communications. An optimization problem is formulated for maximizing the sum rate of both the DL and UL transmissions via jointly optimizing beamforming, receive filters and power allocation, while guaranteeing the sensing requirements and transmission power constraints. However, the formulated problem is a non-convex optimization problem that is challenging to solve directly due to the tight coupling among optimization variables. To tackle this complicated issue, we employ an efficient algorithm architecture leveraging alternating optimization (AO). Specifically, with the given receive filters and transmission power for UL communication, the transmit beamforming subproblem is addressed by successive convex approximation (SCA)-based and penalty-based algorithms. A fractional programming (FP)-based algorithm is developed to tackle the receive filters and transmission power for UL communication optimization subproblem. Extensive numerical results validate the performance improvement of our proposed JAPS scheme and demonstrate the effectiveness of our proposed algorithms.