We give an extensive study on a class of interfacial superroughening processes with finite lateral system size in 1+1 dimensions described by linear growth equations with spatiotemporally power-law decaying correlated noise. Since some of these processes have an extremely long relaxation time, we first develop a very efficient method capable of simulating the interface morphology of these growth processes even in very late time. We numerically observe that this class of superrough growth processes indeed gradually develops macroscopic structures with the lateral size comparable to the lateral system size. Through the rigorous analytical study of the equal-time height difference correlation function, the different-time height difference correlation function, and the local width, we explicitly evaluate not only the leading anomalous dynamic scaling term but also all the subleading anomalous dynamic scaling terms which dominate over the ordinary dynamic scaling term. Moreover, the relation between the macroscopic structure formation and anomalous interfacial roughening of the superrough growth processes is analytically investigated in detail.