The SIS structure---a thin superconducting film on a bulk superconductor separated by a thin insulating film---was propsed as a method to protect alternative SRF materials from flux penetration by enhancing the first critical field $B_{c1}$. In this work, we show that in fact $B_{c1}$ = 0 for a SIS structure. We calculate the superheating field $B_{sh}$, and we show that it can be enhanced slightly using the SIS structure, but only for a small range of film thicknesses and only if the film and the bulk are different materials. We also show that using a multilayer instead of a single thick layer is detrimental, as this decreases $B_{sh}$ of the film. We calculate the dissipation due to vortex penetration above the $B_{sh}$ of the film, and find that it is unmanageable for SRF applications. However, we find that if a gradient in the phase of the order parameter is introduced, SIS structures may be able to shield large DC and low frequency fields. We argue that the SIS structure is not beneficial for SRF cavities, but due to recent experiments showing low-surface-resistance performance above $B_{c1}$ in cavities made of superconductors with small coherence lengths, we argue that enhancement of $B_{c1}$ is not necessary, and that bulk films of alternative materials show great promise.
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