input type ="url" for relative URLs

It says, "While the value of the element is not a valid absolute URL, the element is suffering from a type mismatch."

The spec is still being worked on, but from this quote, it sounds like it could be an issue with Chrome's implementation (bold emphasis is mine):

User agents may allow the user to set the value to a string that is not a valid absolute URL, but may also or instead automatically escape characters entered by the user so that the value is always a valid absolute URL (even if that isn't the actual value seen and edited by the user in the interface). User agents should allow the user to set the value to the empty string. User agents must not allow users to insert U+000A LINE FEED (LF) or U+000D CARRIAGE RETURN (CR) characters into the value.

Source