Pervasive healthcare is a promising assisted-living solution for chronic patients. However, current cutting-edge communication technologies are not able to strictly meet the requirements of these applications, especially in the case of life-threatening events. To bridge this gap, this paper proposes a new architecture to support indoor healthcare monitoring, with a focus on epileptic patients. Several novel elements are introduced. The first element is the cascading of a WLAN and a cellular network, where IEEE 802.11ax is used for the wireless local area network to collect physiological and environmental data in-home and 5G-enabled Fixed Wireless Access links transfer them to a remote hospital. The second element is the extension of the network slicing concept to the WLAN, and the introduction of two new slice types to support both regular monitoring and emergency handling. Moreover, the inclusion of local computing capabilities at the WLAN router, together with a mobile edge computing resource, represents a further architectural enhancement. Local computation is required to trigger not only health-related alarms, but also the network slicing change in case of emergency: in fact, proper radio resource scheduling is necessary for the cascaded networks to handle healthcare traffic together with other promiscuous everyday communication services. Numerical results demonstrate the effectiveness of the proposed approach while highlighting the performance gain achieved with respect to baseline solutions.