This work presents a unified semi-analytical method combining the Numerical Equivalent Inclusion Method (NEIM) and the Distributed Dislocation Technique (DDT) to study the interaction between arbitrarily shaped inhomogeneities and cracks in full- and half-plane domains. By discretizing inhomogeneities into equivalent inclusions and modeling crack surface tractions as distributed dislocations, the method achieves high computational efficiency. Parametric studies reveal that stiff inhomogeneities shield Mode I SIFs but amplify Mode II SIFs, and increasing crack branches significantly alters stress distributions. The method shows less than 3% error compared to FEM, demonstrating its accuracy and suitability for fatigue and reliability analysis of materials with complex microstructures.