Beechjet 400 Captain reported trim control malfunction on departure resulted in temporary loss of aircraft control. Flight crew regained aircraft control and continued to destination.

Narrative

-- Initial climb; SIC (PF) attempted to level off at assigned altitude of 3000'; autopilot (A/P) not engaged. -- I engaged A/P and commanded a vertical speed (VS) descent to try and return to assigned altitude; to no effect. -- SIC disconnected A/P (with an obvious and noticeable nose up kick) and again attempted to force the nose down with physical effort and yoke trim switch. -- I then took controls and also tried physical force and the yoke trim switch; likewise with no effect. -- I directed the SIC to select EMER TRIM (emergency pitch trim) and use the manual trim switch to try and drive the nose down--this did work. -- After we stabilized; Center gave us vectors to keep us in their airspace while we evaluated our situation. -- We re-engaged A/P; and once we were confident that it was working properly we continued our climb and proceeded on course. -- Thank you to our Center controller who kept us climbing and out of everyone's way while we worked the problem. He sequentially cleared us from 3K; to 8K; to 13K; and eventually 20K. Great support and management of our situation.