Sounds like you probably want to use URL rather than URI (which is more general and needs to deal with a less strict syntax.)
URI a = new URI("http://www.foo.com");
URI b = new URI("bar.html");
URI c = a.resolve(b);
c.toString() -> "http://www.foo.combar.html"
c.getAuthority() -> "www.foo.com"
c.getPath() -> "bar.html"
URI's toString() doesn't behave as you might expect, but given its general nature it may be that it should be forgiven.
Sadly URI's toURL() method doesn't behave quite as I would have hoped to give you what you want.
URL u = c.toURL();
u.toString() -> "http://www.foo.combar.html"
u.getAuthority() -> "www.foo.combar.html" --- Oh dear :(
So best just to start straight out with a URL to get what you want:
URL x = new URL("http://www.foo.com");
URL y = new URL(x, "bar.html");
y.toString() -> "http://www.foo.com/bar.html"