Recent molecular communication (MC) research has integrated more detailed computational models to capture the dynamics of practical biophysical systems. This paper focuses on developing realistic models for MC transceivers inspired by spheroids - three-dimensional cell aggregates commonly used in organ-on-chip experimental systems. Potential applications that can be used or modeled with spheroids include nutrient transport in organ-on-chip systems, the release of biomarkers or reception of drug molecules by cancerous tumor sites, or transceiver nanomachines participating in information exchange. In this paper, a simple diffusive MC system is considered where a spheroidal transmitter and spheroidal receiver are in an unbounded fluid environment. These spheroidal antennas are modeled as porous media for diffusive signaling molecules, then their boundary conditions and effective diffusion coefficients are characterized. Furthermore, for either a point source or spheroidal transmitter, the Green's function for concentration (GFC) outside and inside the receiving spheroid is analytically derived and formulated in terms of an infinite series and confirmed with a particle-based simulator (PBS). The provided GFCs enable computation of the transmitted and received signals in the proposed spheroidal communication system. This study shows that the porous structure of the receiving spheroid amplifies diffusion signals but also disperses them, thus there is a trade-off between porosity and information transmission rate. Furthermore, the results reveal that the porous arrangement of the transmitting spheroid not only disperses the received signal but also attenuates it in comparison to a point source transmitter. System performance is also evaluated in terms of the bit error rate (BER). Decreasing the porosity of the receiving spheroid is shown to enhance the system performance. Conversely, reducing the porosity of the transmitting spheroid can adversely affect system performance.