Free-space optical (FSO) channel offers line-of-sight wireless communication with high data rates and high secrecy utilizing unlicensed optical spectrum and also paves the way to the solution of the last-mile access problem. Since atmospheric turbulence is a hindrance to an enhanced secrecy performance, the mixed radio frequency (RF)-FSO system is gaining enormous research interest in recent days. But conventional FSO models except for the double generalized Gamma (DGG) model can not demonstrate secrecy performance for all ranges of turbulence severity. This reason has led us to propose a dual-hop eta-mu and unified DGG mixed RF-FSO network while considering eavesdropping at both RF and FSO hops. The security of these proposed scenarios is investigated in terms of two metrics, i.e., strictly positive secrecy capacity and secure outage probability. Exploiting these expressions, we further investigate how the secrecy performance is affected by various system parameters, i.e., fading, turbulence, and pointing errors. A demonstration is made between heterodyne detection (HD) and intensity modulation and direct detection (IM/DD) techniques while exhibiting superior secrecy performance for HD technique over IM/DD technique. Finally, all analytical results are corroborated via Monte-Carlo simulations.