K2-19b and c were among the first planets discovered by NASAs K2 mission and together stand in stark contrast with the physical and orbital properties of the solar system planets. The planets are between the size of Uranus and Saturn at 7.0$pm$0.2 R_E and 4.1$pm$0.2 R_E, respectively, and reside a mere 0.1% outside the nominal 3:2 mean-motion resonance. They represent a different outcome of the planet formation process than the solar system, as well as the vast majority of known exoplanets. We measured the physical and orbital properties of these planets using photometry from K2, Spitzer, and ground-based telescopes, along with radial velocities from Keck/HIRES. Through a joint photodynamical model, we found that the planets have moderate eccentricities of $e approx0.20$ and well-aligned apsides $Delta varpi approx 0$ deg. The planets occupy a strictly non-resonant configuration: the resonant angles circulate rather than librate. This defies the predictions of standard formation pathways that invoke convergent or divergent migration, both of which predict $Delta varpi approx 180$ deg and eccentricities of a few percent or less. We measured masses of $M_{p,b}$ = 32.4$pm$1.7 M_E and $M_{p,c}$ = 10.8$pm$0.6 M_E. Our measurements, with 5% fractional uncertainties, are among the most precise of any sub-Jovian exoplanet. Mass and size reflect a planets core/envelope structure. Despite having a relatively massive core of $M_{core} approx15$ $M_E$, K2-19b is envelope-rich, with an envelope mass fraction of roughly 50%. This planet poses a challenge to standard models core-nucleated accretion, which predict that cores $gtrsim 10$ $M_E$ will quickly accrete gas and trigger runaway accretion when the envelope mass exceeds that of the core.
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