It seems like a very strange way to define brown ales, lumping them in with porters simply because they utilize some roasted malt. A lot of different beers use roasted malts, in various levels of color and flavor and in various amounts. Defining beers by ingredients is a little backward, IMO. In most cases, beer styles "evolved" based on local factors, especially the available water. Brown ales, like Munich dark beers or porters, were originally produced with water supplies that not only created a darker, more aromatic mash (and therefore, beer) but produced off-flavors in beers with high hopping rates.

Part of your problem may be that we have no history with "mild" here in the US, but milds are much more closely related to brown ales than are porters. Getting a definition of "mild", even in the UK where the style persists (deliciously) is nearly impossible, but historically a brewery could produce a "mild" and a "bitter" in which the defining distinction was the hopping rate. Milds tend to be darker than bitters but the noticeable roasted character of a porter or stout is lacking, and the emphasis is on malt flavor, as it is in the better-executed brown ales.

UK top-fermented beers fall loosely into: brown/mild, bitter/pale ale, porter/stout -- with diversions into "old" ales and other oddities.