Your husband is generally right: when a fence has a clearly finished or “pretty” side and an unfinished side with posts and rails, the finished side usually faces outward toward the neighbor, street, or public area. This is standard fence etiquette, and in some cities it is actually written into local rules. For example, Miami-Dade County requires the finished side to face the neighboring property or street, and other municipalities have similar requirements.
There’s a practical reason too. The side containing the horizontal rails and posts can sometimes provide easier footholds for climbing, so keeping those structural pieces on your side may offer a little more security. It also gives you easier access to the supports when repairs are needed. From the neighbor’s perspective, they see the cleaner, flatter side rather than exposed framework.
That doesn’t mean every fence everywhere must be installed this way. Local zoning rules, homeowners-association requirements, property-line agreements, and the type of fence can all change what’s allowed. Some modern “good-neighbor” fences are designed so both sides look nearly identical, which avoids the issue completely. Before installation, it’s also smart to verify the property line and check for easements or permit requirements.
So if you want the attractive side facing your own yard, you technically might be able to do it depending on where you live—but it could create problems if local rules require otherwise. The safest traditional approach is simple: pretty side toward the neighbor, posts and rails toward your own property.