What you want is back to base monitoring where your alarm system will 'check in' with your alarm monitoring company every 'x' minutes/hours to confirm that everything is still functional and that 'nothing has changed'.
If your concerned about phone lines being cut and signals being jammed you should be similarly concerned as to how the attacker knew the location and specifications of all your systems. GSM, 3G and 4G (and depending on country, CDMA) signals will all need to be blocked as the frequency bands are actually quite wide and these days quite difficult to block unless your attacker is a electronics engineer (that being said, most jammers are fairly low powered unless you have $$ to spend).
It should be possible to harden phone lines (up to a point buy digging them deeper, putting sensors around them, limiting access etc) but at some point they'll always run into the street so there's not much you can do about it if the attacker is determined.
As Uwe says, redundancy is your best bet, layers of different defences will make the system resilient against attacks but nothing is perfect. That's why banks get attacked. If your house is using multiple forms of alarms and CCTV however, its unlikely that you'll be targeted for a 'general' break and enter as it's to much effort for an opportunistic thief