Firstly let me say that below isnt meant to be me preaching or anything else, I have tried to rewrite it to make it less preachy (but I failed!) but to be honest it is a pretty important subject - so please dont take it the wrong way!
I dont think that 350k is anywhere near enough.
I have over a million in life and trauma insurance, income protection insurance and MBF loss of licence insurance - and I think I am under insured. Thats not me bragging - I mention it as an indication of how much I reckon I want to have available for my wife and kids if anything happens to me. Granted I am not being paid GA salary levels, but I reckon go for as much as you can reasonably afford.
The problem is that if you are gone, or worse still, there but in need of constant care, 350k will last about a year.
You need enough dough to pay off the house or buy one if you dont have one, pay off your debts (credit cards, student loans, cars, personal loans, the store account for that large LCD tv you thought was a bargain), if you have kids you need to be able to hire a nanny or babysitter (or child care) so that your partner can earn a living to support the kids and or you. You need to dress, feed and educate any kids and that all takes money.
If you dont end up dead - thats when you really need money. Medical benefits will only go so far, and after that it is your pocket that needs to support you into your dotage.
I recommend that you speak with a reputable financial planner, work out what you need to support your family if anything happens to you.
Dont underestimate how much it costs to support a family.
They have to cope with you not being there to see all the important milestones - they dont need to be saddled with your debt and they dont need to be left in poverty.
I hope you sort it all out - it is a pretty important piece of the financial puzzle.
Good luck