We propose and experimentally demonstrate the feasibility of an integrated hybrid optical fiber sensing interrogation technique that efficiently combines distributed Raman-based temperature sensing with fiber Bragg grating (FBG)-based dynamic strain measurements. The proposed sensing system is highly integrated, making use of a common optical source/receiver block and exploiting the advantages of both (distributed and point) sensing technologies simultaneously. A multimode fiber is used for distributed temperature sensing, and a pair of FBGs in each discrete sensing point, partially overlapped in the spectral domain, allows for temperature-independent discrete strain measurements. Experimental results report a dynamic strain resolution of $7.8\mathrm{n\epsilon }/\surd \mathrm{Hz}$ within a full range of 1700 με and a distributed temperature resolution of 1°C at 20 km distance with 2.7 m spatial resolution.