A new state observer-based current balancing method for Modular Multilevel Converters with Interleaved half-bridge Sub-Modules (ISM-MMC) is presented in this paper. The developed observer allows estimating currents through interleaved half-bridge legs in each submodule of ISM-MMC basing only on arm current and submodule's capacitor voltage measurements. Then, the interleaved current balancing control uses the estimated currents to reduce the interleaved currents imbalance caused by upstream control actions. This technique minimizes the number of required current sensors in ISM-MMC, thereby reducing the converter's cost, weight, and volume. Capabilities of the proposed sensorless interleaved currents balancing control has been tested against standard parameter tolerances of the composing passive elements. In addition to that, a novel capacitor voltage balancing strategy for MMCs is developed. The new algorithm contains main advantages of the classical sorting-based capacitor voltage balancing methods while provides an opportunity to decouple two balancing tasks of ISM-MMC, namely capacitor voltage and interleaved legs current balancing. The feasibility of the proposed methods is verified by extensive simulation and experimental tests on a laboratory prototype by the corresponding system response under the output characteristics variation and interleaved current control perturbation.