It's best to have dedicated characters.
That will make it easier at least.

Each sub-profession only takes a few months to perfection.

Well, this is my first post, but I'll be playing my main character as my dedicated
miner/harvester/industrialist and have my alt setup as my combat character.
(been playing 7-8 days now and just subscribed)

Yes, they will have to share the EPs, but each character starts off with basic
training in his specialty (mining or combat in my case) and I'm training them up
together.

Right now Makkus makes all the ammo to support my combat char's (Brutus) light
and assault mech's guns.  Thats the only real support he needs as he sells off everything
he loots except for kernels and occasional items to pass on to Makkus to reverse engineer
and make CTs from.

Only been playing about 8 days now and Makkus will have his Termis (mining mech)
tomorrow (currently using Argano & Laird for mining and harvesting).  I'd be a bit further
along except I lost my first Argano and gear getting swarmed by npc mechs while returning
from artifact hunting.  Had to rebuild and replace my lost mech and equipment.

So, yeah my combat guy will advance a bit slower but my indy guy will be able to make
or buy him just about anything he needs as he levels up.  I'm not worried about getting
past the industrial mechs into heavy ones, so my skills will shortly be where I want them
for mining and industry.
Then all EPs go to Brutus to advance his combat skills.  Honestly, I consider it setting up my
combat character's money making first for a mere short 2-3 week delay in his initial EP flow.

I'd rather have the money waiting for him when he needs it as his skills advance.

my 2 cents worth anyway.   :-)

Need to be a little more specific about which style of combat and which part of indy your interested in.

The simple answer is what Shaedy says, don't cross the streams!

But, there are some cases where you can progress with combat and iny on the same account, and not be fully gimped.

First, if your looking to PVP style combat, then don't cross train. The bredth of skills you need to pickup beyond just weapons makes it really difficult to be competitive against other players that are focused on PVP.

In other words, if you looking to PVP, its hard enough to be competitive. Don't make it harder by trying to do it part time.

Now, onto things that do make more sense.

Bot based indy like gathering/transport and PVE combat are an OK mix, as there's some overlap in robot EP (reactor /CPU/Acc).

Indy production, is interesting. You can start production lines and they will run while you are out doing combat. So in essence, its one of those mixes that allow you to be doubly productive, where with mining, your doing that or combat only.

The downside is that indy production needs ALOT of EP to be cost effective. Meaning, it could cost you MORE to make your own bots then it would be to just buy them from producers with higher skills. And none of that EP overlaps with combat, so your really slowing down progress if you choose this combination. Probably because, as I point out, its doubly effective

Thanks guys.
Im just going to go with two subs. For the price it just makes sense.