Intermittently connected mobile networks (ICMNs) serve as an important network model for many critical applications. This paper focuses on a continuous ICMN model where the pair-wise contact process between network nodes follows a homogeneous and independent Poisson process. This ICMN model is known to serve as a good approximation to a class of important ICMNs with mobility models like random waypoint and random direction, so it is widely adopted in the performance study of ICMNs. This paper studies the throughput capacity and delay-throughput tradeoff in the considered ICMNs with Poisson contact process. For the concerned ICMN, we first derive an exact expression of its throughput capacity based on the pairwise contact rate therein and analyze the expected end-to-end packet delay under a routing algorithm that can achieve the throughput capacity. We then explore the inherent tradeoff between delay and throughput and establish a necessary condition for such tradeoff that holds under any routing algorithm in the ICMN. To illustrate the applicability of the theoretical results, case studies are further conducted for the random waypoint and random direction mobility models. Finally, simulation and numerical results are provided to verify our theoretical capacity/delay results and to illustrate our findings.