As per the stib-mivb.be website, a MOBIB card can be bought through the online sales channel “GO easy” (requires a, presumably Belgian, electronic identity card), but this is not mentioned as an option for the MOBIB Basic cards, which are available only at a KIOSK or BOOTIK sales outlet:
A MOBIB card costs €5 and has a validity period of 5 years. It can be bought in a BOOTIK or through GO easy. If you wish to buy a personal MOBIB card, you will need your electronic identity card (eID), a recent identity picture and €5.
A MOBIB Basic card costs €5 and has a validity period of 5 years. It can be bought in a KIOSK, in a BOOTIK. The purchase of this card does not require any administrative formality.
The site has a list of KIOSK and BOOTIK sales outlets. There’s a KIOSK at each of the three major Brussels railway stations (Brussels-North, -Central and -South; at the connected metro or underground tram stop). Brussels Airport Zaventem has neither a KIOSK nor a BOOTIK.
Besides the official STIB-MIVB sales channels, some tickets can be bought at supermarkets and other shops. These can be found using the store locator, where you can enter an address and select what you are looking to buy, but this does not offer either MOBIB (Basic) cards or “JUMP 48h” tickets as an option. It does have an option though for “Discover Brussels 24,48 and 72 hours.”
Technically, you could also buy a MOBIB (Basic) card from Belgium’s other public transport operators. But TEC is the only one that offers MOBIB Basic, and they have no “Espace TEC” sales point in or around Brussels. The other two (De Lijn, SNCB-NMBS) only offer MOBIB cards, and I’m not sure whether they will sell you one if you’re not also buying a month or year pass for their network.
Please keep in mind that while the question talks about the “JUMP 48h” tickets as “a very cost effective way of traveling inside Belgium”, these tickets are only valid for travel within Brussels:
Geographical area: the MTB area, i.e. the entire STIB network (including the Bourget-Brussels Airport section) with the possibility to change lines, (ii) the TEC and De Lijn urban networks in the Brussels-Capital Region and (iii) in 2nd class the SNCB rail network in the Brussels-Capital Region.
Note that Brussels Airport (Zaventem) is outside of the Brussels-Capital Region. So a “JUMP 48h” ticket is valid for travel from and to the airport using STIB-MIVB buses only, trains and buses of the other operators (SNCB-NMBS, De Lijn, TEC) are excluded.