An extension of the Share-a-Ride Problem is proposed, which explores the coordination of ride-hailing vehicles (RVs) and logistic vehicles (LVs) for integrated passenger and parcel service. The goal is to investigate the extent to which RVs can increase profits and logistic companies can reduce operational costs, via information sharing and vehicle coordination. A new optimization problem, termed the Share-a-Ride problem with ride-hailing and logistic vehicles (SARP-RL), simultaneously determines the LV fleet size and passenger/parcel request assignment, assuming that passenger requests can only be served by RVs while parcel requests can be served by both RVs and LVs. The goal is to maximize the total RV profits while minimizing logistic costs. An exact solution framework is proposed by (1) generating all trips for the entire set of passenger and parcel requests via an efficient enumeration method; and (2) finding Pareto-optimal solutions of the bi-objective problem via an epsilon-constraint method. A case study of the Manhattan network demonstrates the solution characteristics of SARP-RL. The results indicate that: (a) the SARP-RL can increase total RV profits by 11.93%-27.65% and reduce logistic costs by 47.63%-81.06%. (b) The novel enumeration method achieves computational savings by over 80% compared to Alonso-Mora et al. (2017) approach. (c) Key factors influencing the performance of SARP-RL include the RV fleet size, spatial distribution of parcel requests, passenger/parcel request ratio, unit price of transport service, vehicle capacity, and passenger service requirements, which are quantitatively analyzed to offer managerial insights for real-world implementation.