The bipolar low-voltage DC (LVDC) distribution system has become a prospective solution to better integration of renewables and improvement of system efficiency and reliability. However, it also faces the challenge of power and voltage imbalance between two poles. To solve this problem, an interface converter with bipolar asymmetrical operating capabilities is applied in this paper. The steady-state models of the bipolar LVDC distribution system equipped with this interface converter in the grid-connected mode and off-grid mode are analyzed. A control scheme based on DC offset injection at the secondary side of the interface converter is proposed, enabling the bipolar LVDC distribution system to realize the unbalanced power transfer between two poles in the grid-connected mode and maintain the inherent- pole voltage balance in the off-grid mode. Furthermore, this paper also proposes a primary-side DC offset injection control scheme according to the analysis of the magnetic circuit model, which can eliminate the DC bias flux caused by the secondary-side DC offset. Thereby, the potential core magnetic saturation and overcurrent issues can be prevented, ensuring the safety of the interface converter and distribution system. Detailed simulations based on the proposed control scheme are conducted to validate the function of power and voltage balance under the operation conditions of different DC loads.