We present a new paradigm for performing remote haptic-robot interactive operations. The new paradigm is anchored on an architecture that combines local autonomy with a high-level exchange strategy of reference input. This represents a departure from the conventional reliance on direct exchange of low-level control signals in a global feedback control system. The new approach establishes two local autonomous controllers acting on the robot and the haptic device, interfaced at a higher level via a dual-proxy model. The dual proxy is a passive bridge between the local autonomous controllers. It generates appropriate motion and force reference inputs that are consistent with the task physical interactions and the levels of autonomy. Its model is adjusted online with respect to exchanged position, contact, and environment geometry information. A key component in this methodology is the perception algorithm on the robot side, the Force-Space Particle Filter, designed to reliably estimate in real time the environment contact geometry. The series of simulations and physical experimental validations of the approach demonstrate the transparency and high fidelity in haptic-robot interaction and its inherent robustness to communication delays.