The accreting millisecond X-ray pulsar Swift J1756.9-2508 launched into an outburst in April 2018 and June 2019 - 8.7 years after the previous period of activity. We investigated the temporal, timing, and spectral properties of these two outbursts using data from NICER, XMM-Newton, NuSTAR, INTEGRAL, Swift, and Insight-HXMT. The two outbursts exhibited similar broadband spectra and X-ray pulse profiles. For the first time, we report the detection of the pulsed emission up to ∼100 keV that was observed by Insight-HXMT during the 2018 outburst. We also found the pulsation up to  ∼60 keV that was observed by NICER and NuSTAR during the 2019 outburst. We performed a coherent timing analysis combining the data from the two outbursts. The binary system is well described by a constant orbital period over a time span of ∼12 years. The time-averaged broadband spectra are well fitted by the absorbed thermal Comptonization model COMPPS in a slab geometry with an electron temperature, kT_e=40-50 keV, Thomson optical depth τ ∼ 1.3, blackbody seed photon temperature kT_{bb, seed}  ∼0.7-0.8 keV, and hydrogen column density of N_H ∼ 4.2x10²² cm^-2. We searched the available data for type-I (thermonuclear) X-ray bursts, but found none, which is unsurprising given the estimated low peak accretion rate (≈0.05 of the Eddington rate) and generally low expected burst rates for hydrogen-poor fuel. Based on the history of four outbursts to date, we estimate the long-term average accretion rate at roughly 5x10^-12 M_⊙ yr^-1 for an assumed distance of 8 kpc. The expected mass transfer rate driven by gravitational radiation in the binary implies the source may be no closer than 4 kpc. Swift J1756.9-2508 is the third low mass X-ray binary exhibiting "double" outbursts, which are separated by much shorter intervals than what we typically see and are likely to result from interruption of the accretion flow from the disk onto the neutron star. Such behavior may have important implications for the disk instability model.