No, you should not expect that the two different providers of cable TV / DOCSIS services will just happen to have frequency allocation plans where nothing conflicts. It's generally a bad business practice for a provider to waste capacity on their cable, so they use every frequency their cables can carry, and for typical RG6 or RG59 75Ω coax, that's usually only from DC (0MHz) to 1GHz. At 6-8MHz per channel, that's something like 125-160 RF channels.
Most (?) cable TV systems still think of their cable's RF bandwidth as being segregated into channels of the traditional TV channel widths from the analog broadcast days of a half-century ago. But now a single 6-8MHz channel can carry 1~4 compressed digital video streams, or several dozen digital music streams. Some channels carry "TV network" video or "digital music station" audio streams all the time, some are used for providing "On Demand" and "Pay Per View" streaming, and some are used as DOCSIS downstream data channels. When one of those 6-8MHz RF channels is used as a DOCSIS 3.0 downstream channel, it supports something like 38Mbps (in the 6MHz North American case) of downstream bandwidth, and multiple 6-8MHz RF channels can be aggregated to provide faster levels of service.
It's conceivable that you could pay a consulting RF engineer with CATV/DVB-C and DOCSIS expertise to discover what frequencies the DVB-C provider uses for the TV channels you care about, and what frequencies the DOCSIS provider uses for the upstream and downstream DOCSIS channels, and if the DOCSIS channels and the DVB-C channels you care about don't overlap, he could set you up with the right filters and combiners to combine signals from both services onto one cable without conflict and without accidentally back-feeding anything to either provider. For example, if it turns out that all the TV channels you care about from the TV service provider are below 500MHz, and if it just so happens that your separate DOCSIS provider provisions all their downstream DOCSIS channels above 500MHz, then you could put a low-pass filter (allowing frequencies below 500MHz to pass through, but blocking frequencies above 500MHz) on the TV provider's cable, and a high-pass filter (allowing frequencies above 500MHz to pass through, but blocking frequencies below 500MHz) on the DOCSIS provider's cable, and then combine those two filtered feeds onto a single cable. The cost of the filters and combiners won't be much, but consulting fees would probably be a bit much.
It might cost a lot less to pay a professional cable installer to pull a new coax line where you need it instead of trying to make it all work on a single line. In fact, many cable TV and DOCSIS providers expect to have to pull some cable in every new install, and their standard new customer installation fees cover pulling some amount of new cable through your walls (or providing a new drop from the utility pole, or whatever applies in your situation. And really, you only need the coax from the DOCSIS provider to reach one place where you'll put your cable modem / gateway, and you'll hook an Ethernet LAN port from the cable modem/gateway to an Ethernet switch and feed it into your existing Cat 6 Ethernet infrastructure.
