Recent work introduced the concept of human teleoperation (HT), where the remote robot typically considered in conventional bilateral teleoperation is replaced by a novice person wearing a mixed-reality head-mounted display and tracking the motion of a virtual tool controlled by an expert. HT has advantages in cost, complexity, and patient acceptance for telemedicine in low-resource communities or remote locations. However, the stability, transparency, and performance of bilateral HT are unexplored. In this article, we, therefore, develop a mathematical model of the HT system using test data. We then analyze various control architectures with this model and implement them with the HT system, testing volunteer operators and a virtual fixture-based simulated patient to find the achievable performance, investigate stability, and determine the most promising teleoperation scheme in the presence of time delays. We show that instability in HT, while not destructive or dangerous, makes the system impossible to use. However, stable and transparent teleoperation is possible with small time delays ($< \text{200}$ ms) through three-channel teleoperation, or with large time delays through model-mediated teleoperation with local pose and force feedback for the novice.