This work introduces a new set of energy-balance-based criteria for the vertical growth of a plain-strain planar hydraulic fracture across a horizontally laminated reservoir formation with heterogenous layer properties and multiple weak interfaces. Combined with Coulomb's friction law for mechanical balance along sliding interfaces, these criteria were built into a novel semi-analytical model of fractional fracture height growth. The model was then applied to investigate the growth of hydraulic fractures in an idealized symmetric three-layer rock formation, with the upper and lower layers acting as barriers to the growth. Preliminary modeling results show how the vertical growth of a hydraulic fracture is influenced by the various mechanical/energy barriers. Three primary types of barrier behaviors are identified. A stress barrier leads to gradually increasing fluid pressure when the barrier layer is crossed. A toughness/modulus barrier, on the other hand, results in an immediate sharp increase in fluid pressure followed by gradual decline in pressure. The effect of individual sliding interfaces is similar to that of a toughness/modulus barrier. The cumulative effect becomes more important when multiple closely spaced interfaces are present. A formation layer containing multiple closely spaced weak interfaces behaves collectively much like a stress barrier.