Actually, a router is a router, and "modems" no longer really exists...
The very concept of "modem" is outdated. What your router does it's all every router has always did - interconnect two different networks and unserstand what packets should be routed to and from, performing transport layer translation if and when needed.
Those network can also use different physical transport technologies (and even logical), and the translation functionality is not exactly to be a "modem" - lots of router always converted Ethernet to FDDI or ATM or whatever you needed. What you call a "modem", one with a "WAN" port (ADSL, whatever) and a LAN port (Ethernet) is actually a "simple" router.
But SOHO "routers" are far more than that. They are also switches, access points, DNS servers, DHCP servers, VPN servers, firewalls, etc. etc., all with their managment interfaces. And here often lies the problem, not in the routing functionality itself.
You can easily disable amd/or not use all of the above functionalities and greatly reduce the attack surface, and move them on devices beyond the router - of course it comes at a price - complexity, noise, power consumption, etc. etc.
But what you really meant is "having a router and all other functionalies as separate devices".