In this paper we explore the concept of an all-wireless Network of Femtocells (NoF). A NoF can be seen as a wireless mesh network providing multi-hop connectivity amongst femtocells and, in turn, to the Evolved Packet Core (EPC). As specified by 3GPP Technical Specifications (TS), IP networks are used to transport data through any interface and, in particular, through the S1 interface in the Evolved Packet System (EPS). More specifically, the transport network layer of the NoF acts as transport for the control- and user-plane data through the S1-MME and S1-U interfaces, respectively. This novel scenario requires specific algorithms for the optimal routing of packets through the S1 interface within the NoF. In order to do so, we propose DiPUMP, a distributed and stateless routing protocol based on backpressure theory. Up to our knowledge, DiPUMP is the first protocol proposed to support control- and user-plane data routing in an all-wireless NoF. We also compare DiPUMP to AODV-ST, a tree-based routing protocol taken as representative for routing protocols commonly found in data networking scenarios that are equivalent to NoFs. Our evaluation results show that, on average, DiPUMP is able to transfer up to a 30% more traffic load than AODV-ST. Finally, we describe the implications of the NoF paradigm and DiPUMP in the 3GPP architecture.