That is correct.That is interesting, as it differs from British usage, AFAIK (which is what most English speakers tend to default to). In British usage (IIRC), the Military Title comes first, then the full (highest) Noble title, such as General Lord Cornwallis, or General The Viscount Dundee.
I'd add that in British usage only the highest title would be used, but initials of any orders of knighthood would be appended after the title, followed by initials of any decorations. Subsidiary and lower titles would only be given during a (very) formal introduction.
If the name of the peer is included, the order would be [rank title][name][highest noble rank][knighthoods*][decorations*][appointments*], eg. Field Marshall Bernard Law Montogomery, 1st Viscount Montgomery of Alamein, KG, GCB, DSO, PC, DL
(KG = Knight Companion of the Order of the Garter; GCB = Knight Grand Cross of the Order of the Bath; DSO = Distinguished Service Order; PC = member of the Privy Council; DL = Deputy Lieutenant**)
* NB - UK ones only
** of Southampton