The consensus is that there is a coat of plates or solid breastplate under that coat. So from inside out it's a shirt -> arming doublet -> maille shirt -> breastplate or coat of plates -> jupon.
The jupon, or surcoat, is a tightly fitted coat that covers the breastplate in order to display your heraldry. It was a fashion thing that would go out of style around 1415 when they stopped covering their armor and thus was born the 'White Harness,' because it was uncovered and the steel showed.
The reason it's believed there's a breastplate under those coats you're seeing mid to late 14th century is because they exist in inventories, they exist in archaeological finds and on statues, and if you look closely at the effigies they all have a very tight waist with a very orb like globose chest. This is consistent with the style of breastplate that existed at the time.
That tight jupon is also an English thing. The French had a version with short sleeves, other countries followed regional styles.
Browse that website I provided in my guide:
http://effigiesandbrasses.comAlso
http://manuscriptminiatures.com is another excellent resource for illuminated manuscripts searchable by the same parameters, as is
http://armourinart.comYou can search by time and region to help narrow down what you like stylistically.
Of course all of this is for naught if you're not after a living history quality kit. In the SCA you can certainly fully enjoy all the SCA has to offer without being as anal about your kit as living historians are. We just find the detail in the kit to be the fun of it as ours is largely a educational endeavor, but no such requirements exist in the SCA.
If historical accuracy is something you're interested in, this research you're starting now is the best first step. The biggest pitfall is wanting to buy buy buy before research research research. It's a very costly and heartbreaking pitfall. If you have any questions on my guide please ask. I intended it for the person new to this hobby, so feedback from someone in your position would be greatly appreciated. It's also kind of a good litmus test to determine if your interest lies in that level of historical accuracy in the first place.