This is actually one of the very few challenges that are legit challenging without having to focus on non stop support power molesting player's patience or just stat stick boosts that make combat miserable for certain factions. The jamming system will make sure that you will have to diversify your forces, otherwise it will be detrimental. Due to the jamming you will be constantly shifting between control groups and responding to enemy counterstrike groups, thus requiring really good micro skill.
While the jammer is hella annoying, there are ways for you to combat against it. If you are playing with minor superweapons, Iron Guards and Iron Curtain cancels jamming. Moreover, vehicles with customization options can somewhat ruin the day for the enemy, as the infantry inside are somewhat aren't affected by the jammer.
Never undervalue defences here. You are facing the 
Russians who have one of the best artillery unit in the game that will rend your defences piece by piece from safe distance, plus the iconic Kirov Airships, who can quickly make short work of your base as well. In addition, 
Haihead will try to sneak their nuke on wheels to destroy your base (if you are playing with an AI, picking the right position is a must, as AI are stupid as hell and doesn't take this nuke seriously), and 
Drillers will constantly causing problems. So make sure your base is stocked with garrison for the moment the defence jamming is on. Make sure to constantly replace them as well, because Haihead will constantly spam Chaos on your units and they will beeline to their instant deaths if you arent constantly baby sitting them.
Without a doubt, Russia is the prime choice for this challenge (as well as every other one). Wolfhounds, SCUDs and Tesla Cruisers completely complement what you need, not to mention the Iron Guards and Iron Curtain mentioned above. Another choice for you is 
Pacific Front, as their Battle Tortoises and to an extent, the Tsurugis, can adapt well to the jammer system (for example, if vehicle jam is on, only the 30mm cannon and the missle launcher of the BT are disabled, while the infantry inside can still rain fire upon the enemy.