Failure of the cellular base station (BS), fully or partially, during natural or man-made disasters creates a communication gap in the disaster-affected areas. In such situations, public safety communication (PSC) providing mission-critical communication and empowered with video transmission capability from the affected area towards the first responders can significantly save the national infrastructure, property, and lives. Unmanned aerial vehicles (UAVs) working as flying base stations (UAV-BSs) are best suited for PSC in such scenarios as UAVs are flexible, mobile, and easily deployable. This manuscript considers a multi-UAV assisted PSC network with an observation UAV receiving videos from the affected area's ground users (AGUs) and transmitting them to the nearby functional ground BS (GBS) via a relay UAV. The objective is to maximize the average utility of the video streams generated by the AGUs upon reaching the ground GBS. This is achieved by optimizing the geographical positions of the observation and relay UAVs, as well as the distribution of communication resources, such as bandwidth, and transmit power, while satisfying the system-designed constraints, such as transmission rate, rate outage probability, transmit power budget, and available bandwidth. To this end, a joint UAVs placement and resource allocation problem is mathematically formulated. This problem is non-convex, which is very challenging to be solved. Considering the block coordinate descent and successive convex approximation techniques, an efficient iterative algorithm is proposed for its solution. Comprehensive simulations affirm that the proposed optimization approach outperforms the results obtained from the previously published related works.